1: Like others said, just unscrew them, they are easy to use, but have a tendency to come undone if you don't lock them with superglue or nail polish (put a drop in the "well" before you screw them tight).
2: My first thought is that it's some kind of modified bit keeper attachment or something like you sometimes see on racehorses. Where the wider part is the browband of the bridle and the 2 buckle ends come down to attach to something that's holding the bit....like a different version of the orange thing on this horse. If that's not it, then I haven't got a clue LOL.
3: I'd take all the buckles off of that and then trash it, it's not super good quality to begin with and it does need some repair work before you could use it even if you did
want to. If you need a working quality bridle for an affordable price, I strongly recommend these
. They are pretty much all I buy.
4: I use a pressure washer and, if needed, a very stiff brush. That gets out the worst of the stuff. I don't like to use soap either because I'm always afraid that I won't get it all rinsed out and it will irritate the horse's skin. If I have a pad get exposed to fungus or something, I normally just throw it away and buy a new one. Much easier that way.
5: No idea, we never really worried about keeping the suede seats of our saddles looking like they did when they were made. I'd normally scrub them with a stiff brush and, if they had a nasty spot, a touch of soap and water, then I'd put an extremely light coat of oil on there...but that changes the color on it, makes it darker.