Side saddle riders do use their legs thank you
generally you'll have a long stick to replace your right leg with when riding aside. Yes to B having their own reins and you'd attach a lead rope or lead rein to lead from A's horse.
In regards to side saddles, you don't actually sit sideways, just swing the hips round and leg round the queen. B will get a very sore right leg and bum as the saddles are harder, flatter and the the hip/leg alignment is like nothing else. You can also swing your right leg down (apron/skirts permissing) to stretch the muscles out. I did this more than usual today as it's been a while since I was last aside!
Ace, you're basically describing a Shetland (standard or miniature, but I'd suggest standard). Yes they need foot care - regular at bigger horses. Generally 6-8 weeks for shod and about every 8 weeks plus for barefoot to keep the balance. If lots of rough ground then they probably self trim so you could go further between trims but they still need balancing. Too many barefoot horses don't get seen frequently enough.
Saddle and bridle is fine and you'll do grand as long as you keep it all clean and oiled. Spurs aren't necessary and should only be used for more refined aids (not for going faster).
They do need their feet picking out daily and before and after riding. Hoof moisturiser is ok to use in dry weather if feet are looking dry and starting to crack but not essential. Google hoof picks and you'll find the device.
You're not going to get rotting feet in mud. You may be more at risk of a bacterial infection called mud fever (not caused by mud but by bacteria found in some bits of mud, but also found in non muddy areas) but that affects the heels and legs rather than foot. You may want to google thrush which is an infection in the frog bit of the hoof.
You wouldn't use open reins to lead - not unless you're a trail riding American, but you wouldn't be side saddle then and they're still not a good way to lead. I'd also not recommend leading with closed/English reins for a few technical reasons. A leather lead rein or a lead rope is fine.
Horses are led from the ground or other horses. Polo ponies are ponied (multiple horses led from one being ridden).
I think that's everything. Just be aware of the differences in terminology and style and standards of care between USA and UK in regards to horses (ie In USA you don't have to be qualified to be a farrier and trail riding is very different to 'English' riding in the USA whech again can be quite different to actual 'English' riding).