Yes, it's still possible to use Usenet independent of GG.
Indeed. I regularly participate in some groups. While just a shadow of its former self, USENET (the text part, never mind the binary groups – those are much used for ahem, redistribution of multimedia content) is still alive and certain groups are rather vibrant.
While the number of ISPs and universities that carry USENET declined almost to zero, several public news servers (aioe, ethernal-september) moved to fill this niche.
What's the relationship between Usenet and Google Groups nowadays? I thought that at some point Google rebadged much of Usenet forums as Google Groups?
You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.