1) Under this configuration it is possible for two users to have the project open at the same time. However, it is not advisable for them both to be working on the same code file at the same time, because every time a user saves the file, the other users will see a prompt indicating that the file has been changed externally. This is likely to be annoying. :-)
2) Yes, but to do this you need to be careful about the permissions. Sharing a git repo among multiple users can cause problems because the files in the .git folder wind up with a mix of owners. Here's a post with more detail: https://serverfault.com/questions/26954/how-do-i-share-a-git-repository-with-multiple-users-on-a-machine
Although it's possible to have users share the local copy of the repo, it is not preferable. It is likely that you can set up a remote repository no matter your constraints; in fact, git can work with a "remote repository" that's nothing more than a folder on a shared network drive. See this article for details:
Finally, you might be interested to know that our just-released version of RStudio Server Pro includes project sharing features that take care of file permissions for you and offer collaborative editing (so you can in fact have two or more people actively editing the same file). More on that feature here:
Hope this helps!