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.
In most courses tips & notes are only available in the browser, but it is totally worth it. After reading the info you can go back to the App. As far as I know only Spanish for English speakers and French for English speakers have T&N available in the App as well.
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"