Here are some of the answers I have for you:
1) Yes you will need to uninstall 12.55 to upgrade or patch as this the new way things happen and the patch doesn't install over the top anymore but actually replaces the installation as all patches are full installers and thus you can install from the patch and be fully installed and patched in one installation step. If you don't uninstall it will prompt you and do so when the installation is attempted.
2) I have no information on 12.61 and don't see it listed anywhere unless you are referring to patch 1 for 12.60 which was just recently released. If this is the case then you can install directly from the patch and 12.60 is not required to be installed first as stated prior all patches are now full installers allowing one to install directly from the latest patch and have all the updates installed upon completion (unless the patch specifically states otherwise within the read me for that patch)..
3) You would open a case with your support provider specifically asking for a new license file for ALM 12.6x version you are migrating to.
4) Not sure exactly what you are asking here as the supported environments page (https://admhelp.microfocus.com/alm/specs/alm-qc-system-requirements.htm#ALM1260) shows several supported Windows environments, The one listed for ALM 12.60 patch 1 specific means that a specific Linux version and build required at least patch 1 to be supported in ALM 12.60 ''officially''. The other listed environments have no minimum patch listed so this means they are supported in all versions and patch levels. I think this is where you are getting confused possibly as several Windows environments are fully supported in ALM 12.60.
I hope this helps,