Is it ok to top off the coolant reservoir while the engine is warm? I opened it slowly and the coolant didn't overflow but I did seem like the coolant level in the reservoir did rise a bit. Do I need to bleed the system now? If so does the engine have to be cold first?

 

If the engine is warm I've always topped it off when it's running.

I have never had to bleed after topping it off, and I only bleed when cold. It's easier messing with cold coolant than hot coolant when bleeding. Bleeding warm just gives you a chance to burn yourself.

I'm no expert though just speaking from personal experience.