let me answer your question one by one marked in BOLD
If I move to 14, I would need the licenses only for the clients right?
Yes, SEPM is just a tool to control the clients and distrubute content and license and it doesn't consume any license
The manager doesn't need a license, although is not clear to me if I can upgrade it using the trial ware version that one can freely download or if I would need to get at least one v14 license to get access to the download of SEMP. As I said, I was not planning to update any clients to v14 at the moment, just the manager, if necessary.
Yes you can user the trial ware license or contact the support team to get your hands on SEP 14 serial number, I assume you have a valid entitlement so it should be relatively easy and free of cost.
In case I move to 14, should I first update SEMP and then perform the backup/remove SEMP/update OS/DR procedure, or first the backup/remove SEMP/update OS/install SEMP14 and perform DS procedure?
As a best practices in an enterprise its always recommended to follow the best practices document (taking the necessary backups) should you need them in case anything goes wrong. so to sum it up take backups of SEPM 12.1.6 and then upgrade to SEPM 14.1.x and then take backups of it as well. then uninstall SEPM and upgrade to win 2016. Then do DR with the backup taken in the SEPM 12.1x environment and see if SEPM 12.1.x works, if its not then you may have to uninstall the current SEPM and install SEPM 14.0
PS: I just read the DS procedure and there is no mentioning of the SQL database settings, is the document assuming the use of the internal database or ar the settings saved in the DS recovery file and restored automatically? I am using a remote SQL server
since you are using a SQL server do a local backup and an SQL backup of both SEP 12.16 and 14 in your SQL studio and in the SEPM server as well and the DR needs to be done from the SEPM server the backup it uses is of its own wizards and it will work with both embedded and SQL.