I might be on thin ice here, but I see no reason why you couldn't (technically, I don't know about license), it's basically a load-balanced setup. In previous versions Community had it's own cache synchronizing. Now it employes the same event distribution system as CMS so perhaps there could be problems in there.
Of course if the sites have different code applying different logic you could get counter-intuitive results (say one site allows comments and the lacks a commenting function, and suddenly the site where it's not allowed gets filled up with comments).
Also, if you use any of the multiplexing/integrating membership providers you should use the same or compatible setup in both sites not to get unexpected results.
And to be clear, I have no experience of such a setup.
Yes this is possible, we're doing just that. Having two separate installations of EPiServer but both using the same Community-database.
Is it technically possible to run a community database on two totally different episerver sites by using the same (related) web.config/community settings and same database specifeid in connectionstrings?