Can you download a game from steam to a USB and then transfer it?

You would likely need to install Steam on the computer you want to use to download the game. Then the big question is whether your school network would even allow you to do Steam downloads (they might have that blocked to avoid people hogging bandwidth). But assuming that you can download the game to Steam, in Steam you can back up the game to USB (assuming it has enough room, and possibly something other than FAT32 file system if any files are larger than the 4 GB file size limit for FAT32. Then you could restore that from the backup file(s) to your other computer, assuming that you log into Steam with the same account.

I think Steams primary copy protection is that you cannot play a non-free game that you do not own unless you buy it, or it is family shared to you by another account who owns it (and is not playing it at that time).