Is there a perfective form of this verb? Děkuji!
There is a perfective verb postarat se, but the meaning is of course slightly different. :)
Why do we write Žofii instead of Žofí?
Because the original name is Žofie in the nominative case and Žofii (with two i) in the accusative case.
Or, shouldn't we just write "Sofie" in English? Or "Zofie"? "Zhofie"?
That probably depends on the girl: what she wants to be called :).
I think the choice they made for Duolingo was to keep things simple and not think about the names (except for getting used to Czech names).
Why do you need "o"? Isn't the verb to take care of?
"Starat se" means "to take care"; in this case "o" would be translated as "of".
Would this also translate to "We care about Žofie"?
Yes, you can try to answer that way yourself.
So this verb can mean TAKE CARE OF and also CARE ABOUT, both?
Isn't Žofie the same name as English Sophie?
They both come from the Greek Σοφία, meaning "wisdom", yes. That doesn't mean they're the same name. Each name is unique.
It is, but we also use Sofie in Czech, that is even closer...
Also, never translate names here.
Well, they are related. But of course they are not the same. If your name is e.g. "Peter" you don't want to be called "Pjotr" or "Pedro".