Whenever I use steam in LoL, It makes it so the shop doesn't work. Is there any way around this?

You don't need to start LoL using steam. You could just go to your riot games folder, (which should be located under Local disk C) and find the EXE file. Right click and send a shortcut to the desktop. If that doesn't solve your problem it may be server troubles.

In a worst-case scenario I'd suggest you re-install, or contact support at support@riotgames.com

If I use the overlay, my clicks don't work...but if I alt-tab and come back to the game my clicks work. If you do use the overlay again alt tab it.

I actually added LoL by a non-steamed game since i don't know if it's out on steam and if it's free, but when i Shift+tab and when I come back in game my click works but my keyboard doesnt can't even alt+tab so i have to ctrl+alt+del >.<
I guess it just not well configured to work with steam yet