<edited, and apologies for any confusion>
Sascha Schmatz - Correct. Exchange Server 2010 is also supported on Windows Server 2012 and 2012 R2 (with Update Rollup 26 for SP3 as we stated here "we’re announcing here that we will support Exchange Server 2010 installed on Windows Server 2012 R2 with the upcoming release of Update Rollup 26 for Exchange Server 2010 SP3. We’re doing that so if you really want to add another Exchange 2010 server to your org, on Windows Server 2012 R2, you can.")
We really don't think customers should start re-deploying 2010 on top of 2012 or 2012 R2 just to avoid the ESU though - that's an awful lot of work. But if a new 2010 server for some reason has to be added to the org, then doing it on 2012 R2 makes sense.
Yes to the other scenarios. Exchange 2010 remains supported until Oct 13, 2020.