I volunteer as a student tech at my school so I've had a lot of time to test some things out that might help you guys.
The easiest thing that I've gotten to work was to use teamviewer and its VPN feature with Firefox. I would have teamviewer installed and running on both my home and school pc (which you can use the one time installation on your school pcs). I would then VPN from my school to home pc. I would then use the VPN information and set it into Firefox. That worked until one of the other student techs physically showed the District IT guys how it worked. Then it got blocked.
Another method that worked was if your home IP or a server you have access to has an unblocked IP on the school network, use OpenVPN. This one takes a lot more tinkering which requires you to set up OpenVPN as a host on your home machine or server then connect it with a client set up on your School PC.
This final method which is one I'm currently testing and working on which has a lot more variables in it. This is more or less if you are in the tech department and have a lot of leniency to do stuff around your school. What you would need is an open internet connection relatively close to the school (There's an Xfinity Connect signal that can be reached from the edge of my school), a router with dd-wrt (we have some extra lying around, but you can pick them up for dirt cheap at a thrift shop), and a wireless adapter. So what you do is go around your school with a phone or laptop looking for an open connection. When you find one set up the dd-wrt router in a classroom or closet that touches the signal. Set the router to work as a repeater so then it extends the connection into your school. Go to the computer you're going to use and connect the wireless adapter to it if there isn't wireless on it already. Connect to the wireless signal, and you're off to the races.
With the exception with web based programming, my school doesn't have any programming courses. I originally learned by starting with simple stuff and figuring out how it worked then move from there with occasional tips from others. A good way to learn a new langauge or part of a language is taking a project or idea you want to make then find similar things people have coded then use that a base of ground to start your idea. For example over the summer, I wanted to make a web based UI to access and watch all my downloaded movies and shows without really knowing any web based languages. So I just started simple and with the basics then went from there. After about two months I ended up with a nice working UI as such.
So it's really just find something to make as you learn because you'll be more enthusiastic about it, get something out of it, and have a better understanding of what you're doing.
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