Oh, fun! It's almost a game! I promise to follow the rules to the best of my ability. I'll also TRY to keep it short. =]
Situation 1 -- I have two answers. It depends on your area.
Where my horse lives and where I ride, the only thing we're going to run into is a deer, MAYBE a coyote, but it won't bother us. So if she does something like that, she is just being difficult. My horse is typically very willing to go along the trails, she LOVES to be out, we go by ourselves all the time. Until she gets tired. Then she behaves in the exact manner you described. I start out by asking her to go forward, with increasing pressure. Then my horse will typically try and turn around, to the left to be specific. I will turn her back to the right and ask her to go forward again. She'll proceed to dance and prance and hop and maybe do a tiny little rear. When I can't get her to respond to my asking for her to go forward, I turn her around, the way she wants to go, and ask her to back up. My horse may not go forward when I want, but she ALWAYS goes backwards. Weird logic for a horse, but it works. So we'll back up a bit, turn to the right, since she likes to turn left, and try to walk on. If she doesn't, we turn around and go backwards again. I repeat the process until she decides it's just easier to walk forwards. It doesn't usually take her too long.
BUT, if I lived in an area where Mountian Lions or Bears were common, I would probably trust my horse and turn around. I'm not about to face something like that.
I think most good riders can tell if their horse is faking a "spook" or not, and I'd suggest to use your instincts.
Situation 2-- Well, my horse doesn't typically spook at rocks, haha. I suppose it's always possible though. First, my horse is more "spooky" leaving than going home, probably because she is so darn excited to be out. If my horse just barely moved over and sped up, I'd probably ignore it. Since I have to walk back the same way I come along the trails, she probably won't be so terrified the second time, or will be too anxious to get home to notice. She's a dork. If she reacts in a larger manner that really catches my attention, I'll turn her around and walk her by this horse-eating rock again and again until she realizes it's just a rock. If she is really "terrified" of this said rock, I'll get off and walk with her up to it, touch it, encourage her to touch noses. She'll probably take about two minutes to "make friends" and then she'll walk on all fine and dandy.
If I were being asked to give advice on the situation, I'd probably suggest they walk the horse back and forth a few times, or introduce the rock and the horse. I know ignoring a little reaction with my horse won't cause her to react bigger or more often, but I can't say the same for any other horse. It's better to be safe than sorry. I think it's importance for the horse to realize that you won't make it do something that will kill it, and I think it helps build the trust between a rider and his mount.
Situation 3 -- For most horses, I find it's a very bad idea to run home. In a lot of cases, it will encourage that barn sour behavior. So, for most horses, I would suggest turning around and walking the horse away from home a few paces, and then turning back. Another strategy is to walk past the gate or path or driveway that means "home." For my horse, sometimes we run back, sometimes we don't. If we are coming back along the main road, we usually walk, maybe trot, very rarely we'll have a nice little collected canter. Coming from the trails, we either walk or come blowing in like hell is chasing us. =]
Situation 4 -- This is where that "go back to basics" thing comes in. To avoid a disaster on the trails, I would request the other riders come back and join us. The next time we went out, I would start working with the horse in a group. If the problem starts on the trails, then I would start on the trails. We'd take a ride down the trail awhile, and part ways. I'd have some of the riders keep going, and some go with my horse and I back towards home. We'd continue with that until he was comfortable leaving the other horses, going towards home and going away from home. Then we'd just go riding with one other horse, and split ways. Again going away from home and towards home alternatively. The idea would be that he learns he is perfectly safe away from the group, and controlling that herd bound instinct.
Situation 5 -- I would start at the beginning. Again. Re-introducing the wash area, the wash appliances, the hose with no water running, the hose with water running, and the noise it makes. I'd take it slow but continue moving along when the horse is comfortable. Then I would have the horse tied in a quick release or a person hold him if they were available. I'd start the hose going, preferably luke warm water, and hose off the hoof of one of his front legs. If he reacts, I will keep the hose on his hoof until he stops moving, for just a second, and take the hose away. Depending on his stress level, I'd try again or wait until the next day. I'd gradually move the hose up his leg and all over his body, waiting for him to take a second to relax before relieving the pressure.
Situation 6 -- I've had a lot of horses do this, it's one of my biggest pet peeves. I'd make sure I had a good strong halter on, preferably a rope halter, or a be-nice halter. I'd catch the horse with a lunge line, so I have more rope, and if the horse bolts, catch him with the lead and turn around, heading back out to the pasture. I think it's important to turn the horse AWAY from you. Respecting your space and all that. We'd continue doing this, leading him to the stall and if he goes even a tad faster than you want him to, turn him back around. Eventually he should learn that going fast means it takes longer. At least that's the idea.
"Great spirits have always encountered violent opposition from mediocre minds."