One of the suggested correct answers was "The arse is his" (chuckle). The British word "arse" only means the same as the American word "ass" when referring to a bum - it does not mean donkey (we Brits call that an "ass" as well).
Now, that's interesting! But it's probably a Duolingo bug, there are no such sentences with 'arse' in the course editor. ;)
No. In the Czech we are given here, the word "ten" is a demonstrative adjective that is followed immediately by the noun that it modifes -- "that ass" or "the donkey".
I'm no expert, but your sentence I would translate as "To je jeho osel".