Do most people have aims and know what they are working towards with their riding?
I think that depends on what you want to do with riding. Personally, I plan on showing at a high level and my instructors know what my goals are and we're working on them. They had me compose an actual list and we sorted it into what needs to be done first, and slowly but surely all of those goals are getting accomplished. Someone who is riding for leisure and doesn't plan on competing at a serious level probably wouldn't have the same goals as me.... although I think everyone should have clearly defined goals.
Sometimes I feel like I'm not sure what's happening, and what I am actually improving on. I know I've got to get better at my cantering and jumping, but I want to be able to do other things as well which I can't. My stables said that I can't ride bareback there (unless I go to pony camp, which I can't afford). I want to be able to learn horse care, but my mum said that I can't help out there or volunteer somewhere because it would get in the way of my school work.
I went a whole year of constant progression then I had two months of the worst lessons of my life. Not only was I not moving forward, I started going backwards so those things happen. You can't always move onto other things until you master the things you've already been exposed to. I wouldn't worry about riding bareback, you're not missing out! If your mom doesn't want you volunteering at the barn to get more experience on the ground working with horses then there isn't much you can do. Just enjoy what you're working on and wait until you're a little bit older.
My lessons just seem random with what we work on, it seems to depend on who else is in my lesson. I really want to do dressage, and perfect all the gaits but I don't think I'll be able to do that at the stables I am at. Sometimes I am on an unbalanced horse, but I'm not really sure what to do about it or how I should ride differently. Sometimes I'm on a horse that is dead to the leg or leans on the reins or rushes at jumps or bucks into canter and I don't know what to do. Am I just being too optimistic, are most lesson horses like this?
You mentioned that you take group lessons previously so you probably don't have a lot of say about dictating what you want to work on. If you can afford private lessons, definitely do them. I only take private lessons and for the most part I control what we're going to work on. I know what you mean about having random lessons and that can be frustrating. You need to at least talk to your instructor about these concerns. It's hard to work on something you're having trouble with if things keep getting switched around.
In most cases if the horse is unbalanced it's because you're riding unbalanced. A lesson barn wouldn't have unsound or horses that have a balance problem, that's just asking for trouble. Only your instructor can tell you what you're doing wrong, it's hard for us to speculate what could be causing the horse to become unbalanced. Like I said before, you really need to spend some time doing no stirrup work especially at the trot and canter. Maybe even take away your reins and work on a lunge line. Yes, I said reins! Cantering without stirrups and reins is a great way to learn balance.
Don't worry about dressage right now because you have to master the basics first. I don't know how long you've been riding but I think you're getting a head of yourself, especially with only 4 hours a month which is very little time in the saddle. It's good though that your barn is switching you up on horses, you do not want to get too used to a specific lesson horse. There will be many times in your life where you will have to ride a dead lazy horse, or one you have to hold back every single stride. It's good experience even if it's frustrating right now. Push button horses are a luxury and when you get used to them you get spoiled. :)
It was a bit annoying that my last "lesson" was actually a hack where we just walked round for an hour and I didn't learn anything because the pony camp was going on and the school was being used. I know that it's nice to get out of the school sometimes and go out into the countryside, but as I only get one hour riding a week I felt like it was a bit wasted, and they could've told me that I would be hacking if my lesson was then so I could have booked my lesson for a different day.
Sometimes these things happen where you show up expecting a lesson and you find yourself doing very light work (hack) for one reason or another. If it happens very rarely I wouldn't worry. I showed up for a lesson last week and found myself riding an unfamiliar horse just to put some miles on it. I didn't learn anything new, we just did basic W/T/C but it was still time in the saddle, and that's always valuable even if you didn't learn something new. Of course, I ride almost every day so I'm not worried about missing out on the odd lesson and I know you don't have that luxury.
It just sounds like you're not happy with your instructor or barn in general, and rightfully so based on what you said in other threads. Do you have another barn you can go to? I also understand you want to ride A LOT but you can't due to your age, time and lack of money right now. Being young sucks at times, but enjoy it while you can. You have your whole life ahead of you to master riding and get into dressage, doing whatever you want. :)