American wanting to solo travel to Germany. Dos and don'ts? Should I rent a car?

I've been wanting to solo travel to Germany for a week from the US in the first week of October. Currently planning to visit Frankfurt, Mainz, Mannheim, Spever, and Heidelberg. I have many questions but l'll leave it to three.

What things should I be aware of?

Should I rent a car or would that be stupid of me to do?

How much of the language should I learn? I know nothing at all, I don't know how to even say thank you or please. I've seen some say that most of the German population is so proficient in the English language I likely wouldn't have to learn anything. However, that seems rather entitled and rude, so l'd like to at least try to know some basics.