Question Overclocking a RX 580

Maybe. Maybe.
One of the most important things to do BEFORE you start overclocking is to get baseline stability and temperature data via torture tests. So, at default everything, run something like furmark and looping unigine superposition, for 2 hours each. Record the max temps and look for artifacts. Once you have that info you'll need to do some research on safe temps for your RX 580.

Only then can you begin to determine the answers to your two questions.
 
PSU is important to know.

I'd start by manually Undervolting each performance state in AMD WattMan. When you go to OC, power and temps are going to strike very quickly if you're running everything on Auto. Bringing the voltage down reduces the power usage and gives you more OC headroom.

My RX480 does 1305MHz @ 1020mV (for reference)

As with any OC, you'll need to stress test to confirm stability.