Hi there, I'm one of the NATS trainees awaiting a return to training. I'll do my best to answer your questions.
1) NATS isn't your only option for ATC but it is your only option for Enroute ATC (the high level stuff, not working in a tower but working in a big building using radar). If you want to do tower or approach you have a couple of options. Firstly, the military is always an option, there are other ATC companies like ANS or HIAL that provide ATC services at different airports, or you can pay to put yourself through the rating and then go and work at an airport that hires controllers individually, like Liverpool.
I don't know when NATS will be opening up recruitment but it should be relatively soon. Obviously that sort of thing is above my pay grade. Suffice it to say recruitment will be re-opening at some point.
A lot of ATC skills are "you have them or you don't" skills. Particularly with radar work, being able to convert a 2D picture on screen into a 3D image in your head isn't really something that's easy to practice. I'd say working on your memory and your multitasking any way that you can would probably be beneficial. It'd also be wise to pick up a copy of the ATC handbook, that was my bible before I went in and does an excellent job covering airspace classification and such. If you want to be a REAL nerd, CAA documents CAP413, CAP493 and CAP774 are the technical documents.
I can only speak for NATS training here but the training assumes no prior knowledge, so while getting a head start can be an advantage, don't worry about knowing what to know beforehand. There are hobbyist networks like VATSIM that you could maybe look into to get some experience, but be careful about picking up habits before going in.
Best of luck if and when you do decide to apply! If you want to chat further, feel free to drop me a message.