Does stat debuff give bonus, too? I.E. cutting its speed

Also, I'd assume your catch rate is greater if you can Paralyze and Sleep?

I don't think that cutting stats (bar HP) make it easier to catch pokemon, also, paralyse sleep would increase the chances, but you can't have them both active at the same time :(

Really? No wonder I couldn't get Sleep to stick after paralizying. /noob

Tynamo has a strong moveset and extremely crappy base stats. Thankfully when it evolves, it goes through major jumps to it's base stats. 

If you're going the way of the Axew, I recommed you trying to catch an Adamant Rivalry Axew.

Yup, the only status condition you can inflict after your pokemon has suffered either Poison, Sleep, Paralyze, Burn or Frozen is Confusion, which does nothing for catch rate (1x).

And yeah, cutting stats does nothing for the probability of catching pokemon, only status conditions (except Confusion), HP differential, Pokeball type and the pokemon's Catch rate (which goes from 255 for pokemon like Zubat, to 3 for the majority of the legendaries).

How does IV and EV compare?

Let's say you catch one with good nature, ie. Adamant, but it end up having crappy IV. Aren't those kind of nullify the bonus?

Crappy IV's means that you'll get lower values in any particular stat with low IV's. Augmenting the EV's in that stat, will somewhat counterbalance that, since for every 4 EV's, you'll have an extra point in that stat (compared to the base value you would have at level 100). So, with a maximum of 252 EV's, you'll potentially have 63 extra points in any particular stat.

Also, the way that IV's affect any stat value depends on the Base stat value as well. A low Base value won't suffer much from low or high IV's, given that it's natural increment would be low as well. For example, a Geodude with 0 IV's, 0 EV's and a hindering nature on Speed, at level 100 would have 40 speed. With 31 IV's, 0 EV's and a hindering nature would have 53 Speed. With 31 IV's, 0 EV's and a beneficial nature would have 89 Speed and with 31 IV's, 252 EV's and a beneficial nature would have 152 Speed.

So, the best of both world is to get 31 IV 63 EV. Does each point in IV translater to 1 point in stat?

Nope, it depends on the base value of that stat. Most of the times it's 2/3 IV's per stat point, but in cases where the base stat is high, like Haxorus's 147 Base Attack value, it's almost 1 IV per 2 stat points (That's why, at level 100, the Attack value can vary betwen 269 to 432).

And to get the best of both worlds is to get 31 IV's and 252 EV's. 4 EV's = 1 extra stat point, 252 EV's = 63 extra stat points.

Okay,

IV = scalable

EV = fixed