Thank you for coming, RoseBlade.
I'm sorry if it's unclear, I'll try to fix it later.
So, replying:
The pokemons nominated on my Want List (4th and 5th gen) can be with any IV, EV, gender, nature and ability. I just want those to fill my dex and boxes.
If you want to offer any pokemon that I do not have on Want List, so then he NEEDS to be breeded/trained.
In this case (Garchomp, Lopunny, some of the monkeys), I want them no matter how. :B
So yes, any IV/EV/Gender/Nature is good to trade. Just pick anything from my Have lists.