I'm new to slack and have the following question. I was initially invited for a team. I set up an account. Now I was invited to join another team. As far as I understood slack is based on teams. That means I can share the same mail address across teams. But if I want to join the second team I can't use the same username. It says I can't pick that username and should try another one. Do I need to choose a different username for every team?
Slack accounts are scoped on a team (tenant) basis, so you can use the same username and email address in different teams - or different ones - all that matters is that the username and email address aren't already in use.
In your case, it sounds like someone else has already nabbed the username you want, so you'll have to choose a new one, or contact an administrator to remove or rename the other user if they're inactive.