I have two computers and would like to download and install the games from my origin account on my new one, which will take days. While this is happening am I able to play the games on the old computer?
No sorry, It will come up with a message saying that you are already logged onto another PC and won't let you do anything. But you can have the same games on different PC's, depending on how many the license allows. So you'll have to decide which PC you want to use to game on.
NB: Preferably the one with higher specs for better gameplay. xD