Yes - remove everything that you can so you don't get paint on the components and do get paint on the bike. A pro place will mask the threads in the bottom-bracket so they don't get clogged.
The 'Folding mechanism' consists of a nut under the hinge and the L-shaped bolt on top, both of which come apart easily with an imperial sized or adjustable spanner.
Removing the kick-stand will be the hardest thing - perhaps you might need to leave this to the pros (if they can do it). One can construct a homebrew tool to get this off (it's the same assembly as on the legendary Raleigh Chopper... see
here] or I've just discovered you can actually buy a reproduction specialist tool for the job. [see
here] but I don't quite know how you'll get it back together if you do this with the former. On my twenty I ground off the whole assembly. There are better, lighter stands available these days anyway. Grinding is a breeze with an angle grinder (took about a minute) but a little longer with a dremel (about 2 hours and several cutting disks
)