Can I put my HD into an enclosure boot into it and expect all my apps / programmes to run? I’ve got to send my laptop, MBP mid 2012, running OSX 10.10, into a repair shop.

I use the computer for work so can’t really be without it. Could I take 5e HD out (this is one of the old MBPs with a removable HD), put it into an enclosure and 5en boot into it to work in from a Mac mini which is currently running 10.13 although I believe it had 10.10 on there at some point so the drivers should be there. 

Would booting into the HD cause any issues with email accounts (imap accessed via Mac mail), Dropbox sync app, and other pieces of bought software that require a serial number ?

I also have file vault enabled on the drive but presumably as long as I know the password I can still boot into it.
The nice thing about macOS is that, so long as the machine you're transferring the drive to is old enough to recognise the OS on it [which it sounds like yours is], it will boot - &amp; you wouldn't even know you'd changed machines.

I migrated my Mac Pro 3,1 to a 5,1 by simply doing that - swap the drive to the new machine. Done.