Hello! Welcome to Wishforege hell xD You can work on multiple badges at once for sure~!

You can do multiple badges at once.

Haha XD and thanks :D

So the evolution methods pokemon doesn´t have to match the type of the badge?

When you're upgrading a badge the pokemon you're evolving have to match the type, though dual types also work (e.g. evolving a grass/fairy type pokemon will help contribute to the fairy or the grass badge, steel type for the steel badge, etc.).

Adding onto this, if a Pokemon evolving gains a type, it will still count for the badge (example: Riolu into Lucario counts for both the fighting AND steel badges, even though Riolu is only a fighting type.)

How do you get the non-gem items required to start upgrading the badges?

You can get relic coppers, silvers, and golds from treasure chests or buy them from players on the marketplace. For the higher tier ones, if you click on your credits, it'll open the credits page and down at the bottom you can convert the lower tiers into higher ones, like you can turn 2 coppers and 4,000 credits into 1 silver. The higher the tier, the more expensive it is to make.

So uh... .. Does anyone got a list of how many gems needed per badge? I just wanna know ahead of time

The Gemwish Badges page has all the information for the badges, but gem total for each badge is 11,500 from Nickel to Wishalloy. Hope it helps!