Is it okay to leave my pc running all day? I left it running at home to download some games.
It's fine. You can pretty much leave it running as long as you want. If you're talking about running it 24/7 you might need to restart once in a while to install updates for example.
It's fine, unless you have an extreme overclock with a high constant voltage. If you are not in the 0.1% of people who do this, by all means leave it on (assuming you don't mind the slightly higher hydro bill).