As above, they are well overdue. Usually they stick because the seals are knackered, and/or there's crud on the sides of the pistons. If you have the correct tools it's not a hugely daunting process if you watch some YouTube videos first. The same principle applies to nearly all types of hydraulic disc brakes. At that age I'd be ordering a new seal kit and doing a full rebuild anyway. It's a lot easier to clean them properly if they're off the bike. You could try the above advice first (pumping out the pistons and cleaning them in situ, then doing a fluid change), but in my experience this is sometimes only a short term fix until it happens again.
I hope when you pump the piston out, your seals don't come out with it. But if they do then you'd have to do the full job anyway.
Regarding the fluid, yes certainly check what type you should use. Use caution and read up on it first, but don't let it put you off, many people are put off doing brakes but they can be done very safely if you have the knowledge, the right tools and follow advice carefully.