IMO group lessons can work with a good instructor when you are just starting out. Not having instructors total attention on you for an hour can give you a bit of breathing space to figure things out. You will know when you need one-on-one when you feel like you haven't learnt anything new for a while.
I also would be looking for a better instructor. I can't imagine that seasoned school horses have behaved badly enough to get kicked in the guts or slapped over the head. Certainly a disgraceful example to students.
A male horse will 'hang out' when he is relaxed. Both geldings and stallions will do it. There is no need to slap them around for it, sometimes just waking them up a making them move is enough to make them retract. I am mainly talking school horses here, I will leave the discussion of stallions at shows out of it.
The seven year old you saw hit the pony. I think we can't turn a blind eye these days especially if you were the only one to see. Even to just say (something like) "that is not necessary, there is no need to be cruel to your pony". She may not like it, and if bad mannered may be rude to you but she will remember being called cruel, and she may start to think about her treatment of her pony, especially if she hears it from others as well. She will also see that other people will not accept bad horse handling.
Not sure if I understood right about grooming/ tacking up, is that part of your lesson time? Maybe it is different for you, and my riding school days are a long time behind me. We could turn up a few minutes before the lesson, ride the due time, tie up and leave. I think we did that exactly twice, then we were early and stayed late, and learned everything we could. In a very short time we were there every spare minute. Sometimes we even 'earned' extra 'free' rides.
As for the guilt thing. There are very few wild herds world-wide. So most horses now either are in domestic 'servitude' or dead, dogfood. Learn well, teach well, and be the voice of an animal that needs it, and these horses will have nothing for you to feel guilty for.
For a smile: well played.jpg