Was I meant to peel anything? If I take the CPU cooler off and put it back on will it effect it?
You shouldn't have needed to peel anything off, no, but yes taking it off will mean that you have to completely clean everything off and start over with new paste. Removing and re-seating disturbs the paste and causes air bubbles which leads to much higher temps.
Oh, noob question but how do I check temps and what is normal?
You can check the temps with any number of programs (you'll need to have Windows installed first, of course). A few that I recommend are HWMonitor, Core Temp and RealTemp.
There really isn't a one size fits all "normal" temp range because of the variables involved (room temp, case airflow, etc.), but in general, with the stock cooler on that CPU, you should idle from 35-45C, and full 100% stress test load should be around 60-70C (maybe a bit higher).