Run second site in the same VM: Is it possible? I would like to run all my Drupal 8 sites in one Vagrant VM instead of just one. Is this possible?

I tried to remove the default drupal site from the "web" folder and pulled(git) 2 of my current probject into it.

For any reason drush does not recongnize the drupal roots as proper drupal sites.

I am not sure how other modules react...  Is it normal to create each time a new VM for each Site you are developing. Seems a bit overkill.
Yes, this is possible, but take it from me as a guy who did it for about 12 sites - it gets tedious fast to manage it.

Setting up and tearing down VMs is so fast and cheap, it's simply more practical to me to create one per project. It's less to manage, and it just becomes a 'part' of the project codebase (you can fetch Drupal VM with Composer now for example, or download and keep it in a 'tools' folder outside of docroot).

Also it does not sound like you are setting up Drupal VM properly... I suggest re-reading the docs or posting more information.