All I can say is having 30-40 a month at age 14 is amazing! I try to get my kids (one older one younger than you) to do chores to EARN money and they want to be lazy, so they don't get it!
I know it is exciting but remember that patients is the key. I know it is hard but will pay off in the long run.
With that lighting I don't know that you will be able to keep much. Possibly the mushrooms because they are low light, but will have to let someone more experienced chime in.
Yes, I would recommend you get the 10g set up as a sump. The more water volume you have the better you will be. With a sump setup you won't need the emperor filter. You should look into DIY overflows that can be made from PVC
. They may not be pretty, but they are in your budget.
One of the more expensive items will be the return pump from the sump. The live rock can also get really expensive but you can cut down on this by getting mostly (like 75%) base rock and then the rest live rock. The base rock will turn live over time.