I did have cases in which my laptop wouldn't charge, but I later found out it was due to the battery not being able to charge anymore. Also, I got an external drive which is where I keep all of my Steam stuff.
But yeah, a school laptop isn't that great at handling 3D games like Gmod, and even then, they would probably simply not allow you to download Steam on it.
Another thing to note is that yes, laptops can heat up a lot when they have to chug so much rendering and data, so it's best to place them where the air can actually escape (also, placing a laptop on your legs is actually a really bad idea, as laptops that get too hot can actually leave a burn on you, so it's best to just place laptops on a desk or table).
