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.
My oldest rig was built in 2006 (with only new GPU's) and I ran it 24/7 since then.
Apart from power costs, it won't hurt anything.
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).
You waste power and add to how much dust it gets in it. There is no reason to leave it on. However it won't hurt anything.