If I buy the sims4 online and install it on my Pc, and eventually I want to buy a new Pc and throw the one I have right now away, will I still be able to play the sims4 in my new computer? Or do I have to pay again for the sims 4?
Yes, you will be able to play the sims4 with Your new computer.
The game is connected to the Origin account & not to the computer.
Note: You may need to copy some savefiles from -the Current computer- to the New computer in order to transfer all of your ingame Work!