Of course it works. Otherwise there would be no ARM on the servers. But it is second class to a setup, where the development and deployment happens on the same platform. Having good ARM machines available on the desktop will give ARM on the server a boost. As I wrote, don't take my word for it, listen to what Linus hat to say on that topic.
Sorry, in general that is not true. You need a very good network connection, both with bandwidth and latency, to make remote devlopment workable. Still, it never equals local development. If you follow the discussions here on hacker news, which terminal software has the smalles latency, remote development never can compete with that.
The only x86 servers were running a mix of NT 4.0 and Windows 2000.
Apparently it worked.