First off, welcome to the kc-mm forums!
Secondly,
1) What happen if I play online with downloaded movesets/textures? (let's say it is wifi safe) what happens on the ennemy's screen? Does it freeze?
KJP forgot to mention some things.
The odds are about 50% that you'll freeze in online play unless you play with friends, as, even though most people will have Project M animations as the character animations, there will still be a lot of people using regular Brawl animations, which would conflict with each other. So I would recommend making sure you're playing online with someone who has your exact same character animations. A similar case with Giga Bowser and increased amount of character palette swaps, as Project M has more of those than regular Brawl, and people play online with Project M and normal Brawl.
By "recolors", KJP meant any textures whatsoever, and I believe by "rigs" he just meant imports and/or vertexes.
I do believe that Mr. Game & Watch textures and/or imports/vertexes won't freeze on wi-fi either, and G&W is
not one-slot, so I think by "one-slot" KJP meant all characters
except G&W.
I think(I'm at least 90% sure of this) some PSAs actually are wi-fi safe, but are limited to retextures of PSAs(i.e. changing the colors of Marth's sword slash or changing what Kirby's pot for his final smash looks like) and imports over the individual objects of PSAs(i.e. Importing/vertexing something over Fox's Landmaster).