Any decent auto machine shop can turn rotors for you. It's not as common as it used to be, because new rotors are so often too thin to turn, but the machines should still be around.
Grooves generally indicate a problem with the pads; like letting riveted pads wear down to the rivets. But since small grooves won't hurt anything, it's possible that someone changed the pads without refinishing/replacing the rotors.
Not sure why pistons stick; seems like sometimes the seal just "becomes one" with the piston. But it's not uncommon for only one to stick.
Triumph calipers are reasonably easy to rebuild; usually the only tricky part is getting the piston started back into the bore with both the dust seal and the hydraulic seal in the right place. But if you split the calipers (which Girling warned not to do), be sure to have new seals on hand to go between the halves. I believe both Moss & TRF have the seals, but they are not usually included in the rebuild kits.
We've debated long and hard over why Girling said not to split the calipers, with no clear consensus. But most of the professional shops do, and I've not heard of anyone having problems from doing so. (Haven't done it myself, as mine are the early one-piece calipers).
The seal rides against the surface of the piston, so make sure the surface is perfect where the seal rides. Any rust or visible pitting is reason to replace the piston, IMO. Otherwise, it's pretty much obvious, I think. Be sure to clean thoroughly, and make sure there isn't any solvent left over inside before you close them up.
Sanding pads seems like a bad idea to me, you wouldn't want to get particles from the sand paper embedded in the pad material to wear out the rotors. Minor grooves won't hurt anything and will quickly wear away anyway, so I'd either leave them or replace the pads.
Last time I bought generic aftermarket organic pads for the TR3, they were horrible, seemed to have no grip at all. My suggestion is to either look for some NORS asbestos pads, or get the 'Kevlar' fiber ones from TSi (which is what I did). They work great even cold, and I've never managed to get them hot enough to notice any fading. Another option is EBC "Greenstuff", but I've heard mixed reviews about them.