- Is there a way to get updates automatically?
SQL Server 2008 R2 is not supported on Windows 10. This means the SQL Server team will not be releasing any security updates or patches if they find any specific issues related to SQL Server 2008 R2 code. There is no way to get updates automatically as none would be released related to Windows 10.
Having said that, SQL Server 2008 R2 installation is not blocked when you try to install it on Windows 10. Of course, it is always better and advisable to install the latest Service Pack (Service Pack 3 is the final SP for 2008 R2).
If you are trying to install SQL Server 2008 R2 for testing purpose on Windows 10, you can go ahead; but since it's not supported it would be of no use to carry forward this idea.
- If not, do I have to install all the service packs in sequence, or can I install only the most recent?
Service Packs are cumulative, so you can directly install SQL Server 2008 R2 SP3 even on RTM bits. There are cumulative updates (CU) released after 2008 R2 SP3 as well, but my advice is don't install CU unless you face specific issues fixed in the CU.