Tangela
1) Is Tangela broken?
Tangela is a no-brainer in my eyes. At the most basic level, Tangela's stats (65/55/115/100/40/60) are simply too good for Little Cup. It can wall anything physical that doesn't have a powerful SE STAB move (Murkrow, Gligar sans item). Even then, check this out:
236 Atk Life Orb Murkrow Brave Bird vs. 236 HP / 236+ Def Eviolite Tangela: 18-26 (69.2 - 100%) -- 6.3% chance to OHKO (18, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 26)
That is perhaps the most powerful unboosted physical STAB move in LC, which Tangela is weak to, and it has the ability to survive it. If you think this spread is uncommon for Tangela, it might be helpful for me to mention that this is the most common defensive Tangela set in use on the ladder according to TIBot. That base 40 Special Defense is a lot less beefy than Tangela's Defense, but it's still enough when combined with it's good HP stat to tank some special hits, such as those from +1 Swirlix, and then put something to sleep with Sleep Powder. A base 100 Special Attack is titanic for a wall, giving it a higher Special Attack stat with no investment than max Special Attack Timid Scarf Snover. Giga Drain from this thing will hurt, and with a Hidden Power Ice or Fire for coverage, it can KO a specific threat such as Gligar while not being close to OHKOed back. Knock Off helps it hit even harder by removing Eviolites. Sleep Powder is what gives defensive Tangela its fear factor, in my opinion. Since it can force so many switches due to its bulk and powerful Giga Drain, Tangela gets a ton of free turns to throw down Sleep Powder to make it very hard to switch into. Even if you have a Yanma or something that can take out Tangela, you are forced to sacrifice a Pokemon to get it in safely, and nothing can stop Tangela from just switching out. Regenerator is the icing on the cake, giving it reliable recovery and removing any penalty to Tangela for being forced out. All of this combines to make a nearly impassable wall that LC would be glad to be rid of.
Sun Tangela with Chlorophyll and Life Orb and LO Regenerator Tangela focus more on Tangela's massive base 100 Special Attack. With Regenerator, Tangela is free to spam LO boosted Leaf Storms from its huge Special Attack and then switch out and regain any health it may have lost from LO and hazards, completely negating the penalties that would normally keep such a set in check. Of course, after using Leaf Storm, Tangela is now forced out thanks to the -2 Special Attack modifier it now has. This isn't always a problem for it, however. Even if it is forced to switch out, it loses basically no health thanks to Regenerator. In addition, the free turn it gives its opponent isn't always useful. If whatever switched in survived, it is definitely weakened a good bit by Leaf Storm. The target is now either forced to Recover, or if it lacks recovery, it must now try to do its job at half health or less. If that job is to check Tangela, then it is no longer capable of it, and will be KOed the next time it tries to switch in. If the target did not survive, this can pose a problem for Tangela if a setup sweeper is able to come in on -2 Tangela. If not, then Tangela picked up a free KO and can now switch out with impunity.
LO Chlorophyll in sun trades the passive healing from Regenerator for pure Speed, allowing it to Speed tie with +1 Yanma and Scarfed 20's like Elekid (this doesn't ever happen but people always mention it anyways). That Speed is the key to this set's success, since otherwise all the 2HKOes that Tangela gets would be harder to get due to its otherwise decent base 60 Speed. In addition, Tangela also gains access to a viable Solar Beam, giving it basically a Leaf Storm that doesn't lower your your Special Attack. Boosted Hidden Power Fire and AncientPower gives Tangela all the coverage it needs. This gives it a 2HKO on pretty much everything in the metagame besides Sap Sippers and 4x Grass resists. As evidence, look at some of the calculations I have compiled here:
196+ SpA Life Orb Tangela Solar Beam vs. 236 HP / 76+ SpD Eviolite Porygon: 16-19 (61.5 - 73%) -- guaranteed 2HKO
196+ SpA Life Orb Tangela Solar Beam vs. 236 HP / 200+ SpD Eviolite Mantyke: 9-13 (37.5 - 54.1%) -- 87.9% chance to 2HKO (highest Special Defense in Little Cup!)
196+ SpA Life Orb Tangela Solar Beam vs. 0 HP / 76 SpD Eviolite Ponyta: 8-10 (38 - 47.6%) -- guaranteed 2HKO after Stealth Rock (Without SR, Solar Beam + AncientPower is a KO)
196+ SpA Life Orb Tangela Solar Beam vs. 36 HP / 20 SpD Eviolite Murkrow: 10-13 (43.4 - 56.5%) -- 88.7% chance to 2HKO
196+ SpA Life Orb Tangela Hidden Power Fire vs. 124 HP / 76 SpD Eviolite Foongus in Sun: 21-26 (84 - 104%) -- 68.8% chance to OHKO after Stealth Rock
196+ SpA Life Orb Tangela Solar Beam vs. 236 HP / 236+ SpD Eviolite Lickitung: 13-17 (46.4 - 60.7%) -- 93.8% chance to 2HKO
These calcs showcase Tangela's power against some of the bulkiest special walls in Little Cup, or against decently bulky resisters like Ponyta. As you can see, none of these walls can switch in to check Tangela without getting 2HKOed in the process. All it takes is for Tangela to get in on something it outspeeds, and then it can just spam Solar Beam as much as it wants. There were a few notable exceptions, such as Vullaby who can withstand Solar Beam + AncientPower, but on the whole, everything I checked was 2HKOed by some combination of Tangela's moves. As a result, this set is harder to revenge kill than either the defensive set or LO Regenerator, because nothing can switch in and outspeed Tangela before it KOes them. Most priority is physical, and even with no investment or Eviolite, they still get absorbed by its huge base 115 Defense.
Tangela's checks and counters are few and far between, and none can handle both sets at once without prior set-up. Yanma is definitely the best Tangela check, since it OHKOes it with a Life Orb Bug Buzz while outspeeding it. With a Speed Boost under its belt, it ties with Modest Chlorophyll Tangela, giving you a 50% chance to beat it, and a 50% chance to be crushed by AncientPower. Outside of that, your best hope is to try and muscle past it. Murkrow and Ponyta have 120 BP SE STAB moves to hit it with, but as I've shown above, the defensive set can live through them and either put them to sleep, Knock Off their items, or put a hurting on them with the correct coverage move, and then switch out to get some health back. Neither of them are capable of switching in, however, so you'll either need to make a sacrifice or a good double switch. Goomy has Sap Sipper to stop STAB Leaf Storms and Sleep Powders, and a Sludge Wave to 2HKO it with, but it's pretty mediocre outside of stopping Tangela. Knock Off will hurt any Tangela set by depriving it of its item, but even so, that could be said of the vast majority of the metagame.
Whether it's defensive or offensive, I'd like to summarize with this: Tangela has high, well-distributed stats, fantastic abilities, the inability to be switched into, and the ability to easily weaken or disable its would-be checks, making it too much for the Little Cup metagame to handle. As this is the case, I see no need to visit questions 2 and 3 for Tangela, as blarajan himself says they are not important if the Pokemon in question is broken.
Yanma
1) Is Yanma broken?
Yanma is a different beast from Tangela, since Yanma's stats don't exactly scream "raw power"(65/65/45/75/45/95). A Base 75 Special Attack is good, definitely usable, but it's not on the level of something we correlate with "hard-hitting" such as Murkrow, Abra, or Tangela. Indeed, Yanma's stats appear good, but not like a top threat in the metagame. In practice, Yanma is a very powerful threat that every team needs solid answers to to be able to succeed. Like Chlorophyll Tangela, Speed is the key to Yanma's success here. Having a max Speed of 20 means it never has to worry about Speed tying anything but the other, uncommon 20 Speeders. This makes Life Orb viable on Yanma, as it no longer needs to carry Eviolite to help it win Speed ties. Now equipped with a Life Orb, Yanma has all the power it needs to deal tons of damage to almost anything.
The Speed Boost set is the set that most people are familiar with, and it makes for an excellent late game sweeper. With Protect to keep it safe for a turn, Yanma is guaranteed to outspeed anything that can't boost its own Speed. After that, it can use STAB Bug Buzz and Air Slash to KO pretty much anything weak to them, and deal tons of damage to frail neutral targets. The main problem with this set is that it is really easy to use; pair it with a reliable Stealth Rock remover and weaken any possible Yanma checks, and it will sweep easily. "But you could say this of any lategame sweeper!" you say, but none can do it as easily as Yanma can. LO Murkrow has Brave Bird recoil and the unreliable Sucker Punch to deal with, making it hard to keep healthy. Swirlix is too slow to begin with, making it more vulnerable before it sets up to Pokemon like Pawniard and Meditite who can threaten it. Berry Juice Gligar relies on getting hit first without dying to boost its Acrobatics, making it a little shaky in a tier where everything carries a random Ice move to screw it over. There is simply nothing in the tier that can just come in and dish out tons of damage like Yanma does.
Yanma's other ability, Compoundeyes, is somewhat underused in this metagame compared to Speed Boost. Rather than sweeping lategame, Yanma can also become an earlygame disruption, using boosted accuracy Hypnosis to put to sleep any slower Pokemon (pretty much all of them) and then either start hitting with LO boosted attacks or set up a Substitute with Berry Juice to earn a free turn to do what it wants. Yanma's Speed stat of 20 means that nothing without Prankster or Scarf can stop Hypnosis from happening, and while sleep got nerfed from Gen 5, it's still enough to earn Yanma an easy free turn. From my experience, the Substitute set does this the best, as a Yanma behind a Sub is much more threatening than the sweeper set could be, since it doesn't matter anymore if Yanma does not OHKO its target, as it can just attack twice and most likely get the 2HKO.
Yanma does have more checks than Tangela though, which makes it a bit easier to deal with. Archen is the best Pokemon for the job thanks to its resistance to Yanma's two STABs, reliable recovery in Roost, and Rock STAB with which to massacre Yanma. Otherwise, Yanma's biggest threats are those that resist Bug Buzz, since it then must rely on the weaker, less accurate Air Slash to deal damage. Gligar, especially Eviolite sets, can easily switch in on Yanma due to its resistance to Bug Buzz and lack of weakness to Air Slash, which is a 3HKO even on Berry Juice sets. From there, Gligar can just use Acrobatics to destroy Yanma. Pawniard is not OHKOed by anything Yanma uses and can use Knock Off to OHKO it with 2 rounds of Life Orb recoil, but it must be wary of switching in. Ponyta can roast it as well, while not being OHKOed by HP Ground. Stealth Rock is a massive problem for Yanma as well, but it should always be paired with a reliable hazard remover, so good players don't always have problems with it.
So is Yanma broken? It's not as clear-cut in my eyes, but I believe that it is broken. The main reason for why this is so is because of Yanma's low-risk high-reward nature. Sweeping with Speed Boost Yanma is not hard at all as long as you don't let your opponent get set up or let Yanma die. Likewise, Compoundeyes Yanma's Hypnosis is all but guaranteed thanks to its huge Speed and boosted accuracy. This makes for a huge threat that isn't hard to play and only requires a few specific checks weakened or removed to succeed. Pawniard, for example, provides fantastic offensive and defensive synergy with Yanma. Pawniard's powerful Knock Off's both tenderize the enemy team and remove their Eviolites and Berry Juices. With those out of the way, Yanma can sweep unimpeded. With the right support, Yanma can easily become too hard to stop, which leads me to believe the metagame would be better off without it.