As I understand it, zorgi corresponds to all of these:

to care Mi ne zorgas. Ĉu li eĉ zorgas pri ĉi tiaj aferoj?

to take care of zorgi pri ĝardeno zorgi pri infano

to worry Mi zorgas pri vi. Kiam panjo ne respondis miajn alvokojn, mi ekzorgis.

I find this very confusing, since all of the meanings are clearly different but still often used in the same context. Take Mi zorgas pri mia avino for example, am I worrying about my grandmother, or am I taking care of her? Also, trying to figure out the meaning of a word like memzorgema is rather tricky.

Are there other words that I can replace zorgi with?