Can someone explain the "ř" in staří to me? Why is it staré and stará, but not starí?
When male animate nominative is plural there's a consonant shift:
They are just completely different and To has several different independent uses/meanings. I suggest to read the Tips and notes.
Oni is the nom. plural masc. animate of on.
To in "to je" "to jsou" is really an integral part of the construction. But in "Dej mi to." it is the neuter complement of the masculine "ten".
This questions repeat almost every day, you will find loads of related answers under other sentences.
If I were to use the other forms of "they" (ony, ona), would I have to change the adjective endings?
Yes. Oni(men) jsou staří, ony (women) jsou staré, ona(děvčata) jsou stará and that all you translate They are old.
Děkuji! Ted' já (how do you say understand?)
But what about zvířata then? I've seen both "oni" and "ony" accepted there
What's the difference between Teď tomu rozumím. and Teď to chápu ? So if I'm talking about female animals, the noun wouldn't change, just the pronoun?
there is no difference in meaning, imho the verb "rozumět" is slightly more formal than "chápat"
as long as the subject is "zvířata", it's always "ona jsou stará", but for example when you talk about a group of cats (=kočky, feminine), you can say "ony jsou staré", but the subject here is "kočky", not "zvířata"