I cannot answer any of the questions because I also have no experience in running a git project.
But what I know is that we are actually less depending on a hoster. Because of git's DVCS nature, everyone has the complete repo locally and can work offline with it. Git hosting is something for convinience (i.e. web interface for source browsing). We wouldn't actually *need* a hoster at all, but of course it would be nice (with hosting, cloning other people's repos is simplified extremely).
This is one of the strong points of git. Even if the hoster is not very dependable, since the actual repo is on everyone's system, the hoster could be dead for a few days or we could switch the hoster easily without losing anything.
Best regards.