Is there some option to list all the SessionId-s created with my API-key?

No, there is not.

Do the unused Session Id-s expire after some period of time?

No, they do not. Sessions do not expire.

If the user actively uses his Session will it be kept indefinitely alive?

Yes.

Is there a max number of active SessionId allowed per API-key?

Nope, unlimited.

How long is the v3 based session management planned to be supported?

I would imagine, given how long it has been online for, it will be supported forever.

Currently I am implementing automated testing for my App, meaning that a bunch of sessions , tokens (resources) are created and abandoned automatically. I dont want to abuse the server or lock myself out.

You don't need to worry about it. There's no limits or restrictions put in place.

Cheers!