Number 2 looks like a one eared headstall. Put the round piece on the leather strip attach the cheek pieces then it should be done lol. I think they have suede cleaner somewhere but I can't be sure. I love the saddle btw:). Posted via Mobile Device
Lean the pad up against something and starting at the top hose it down on hard pressure slowly moving side to side. Mud should start running out the bottom. Don't use soap as it's murder to get out. About all you can do with the rough out is rub either corn starch on it and let it sit. Then vacuum out. It usually helps but if not, at least no harm done.
About the sort of scrungy looking headstall... I would clean it up and put it away in a trunk or someplace where it will stay dry. Down the road you never know when you might need a quick replacement throatlatch strap or whatever.
I keep a few spare parts around for just those sorts of emergencies. Also, go get some replacement Chicago screws to have on hand.
Hose that saddle pad as others have said...no soap.
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.
Number one has been answered but I would never use that bit. IMO it is confusing and worthless.
The picture in number two is a deconstructed headstal or pieces from multiple headstalls for spare parts. You have a brow band, 2 cheek pieces, and a random leather lace or strap. Keep them, you never know when you may need them.
The headstall in picture three has been repaired. Take it apart and put it with the other pieces you have and keep them for spare parts.