My skin isn't visible in any of the lists

You need to accept the Contributor Agreement before your items will be publicly visible, or can be added to the game.

Do the artist see any money from the crates or marketplace?

No. Crates are crafted for free by breaking down other items in your inventory, or by buying them from the marketplace, we don't sell them.

Steam doesn't have a way to split fees from market transfers. This is why a lot of games use the keys system.. in which users purchase keys to unlock crates - and a fraction of the price is split between every skin possible that this key could unlock. Keys don't sit right with us.

Some of the items from last week were removed from the store and added to the crates?

All skins have limited runs. Skins are removed when they've been around for a long time or have made too much money.

This is particularly true with bright skins that we don't want to see everywhere. We want them to be rare and expose a limited amount of them to the world.

If two artists reach the same idea ( which is likely ) and they have similar rates, how would you decide which one to add to the game?

Like everything, whichever is obviously the best, whichever has the most votes, whichever is presented nicer. If one artist hasn't had an item approved before, we'd lean towards approving that artists work. If one of the artists is a general arsehole in the community, we're less likely to approve theirs first.

There seems to be a lot of issues with copyrighted material, what is technically legal in these sense?

It's a matter of opinion a lot of the time. We can't really tell you where the line is without seeing it, things have to be judged on a case by case basis.