"Peter eats his apple."
Translation:पीटर अपना सेब खाता है ।
I'm a beginner in Hindi (and not so good in English), but I felt it's very similar to Japanese "jibun".
If it's the case, the add of "own" to "my", "your" or "his/her/its" (and plurals) is only a didatic way to express it in English for lack of words. In a real world translation, it's not needed, in my opinion.
If we can call "I", "you", "he/she/it" as "absolute" 1st, 2nd and 3rd person, then "apna" would be a "relative 1st person (my)", relative to the context of "apna" is referring to. In this sense, I think "own" transforms for example, "absolute his" to "his own", a "relative my" of 3rd person.
For example, 1) Peter apna seb khata he -> I'm talking about Peter, the context is Peter, so, "apna" is "my" for Peter. Since there's no "relative 'my'" in one word in English, we could just translate as "Peter eats his apple", as suggested by Duolingo.
2) Tumhara apna seb khata he -> I'm talking about you, so, "apna" is "my" for you. Since there's no "relative 'my'" in one word in English, we could just translate as "You eat your apple".
Besides, I don't know yet if Hindi has a "relative you". In Japanese, it's "aite".
Peter ka seb khata hai, is not a meaningful Hindi sentence. It can't be translated but if i had to, it would be - Peter's apple is eaten (by ???).
To make your sentence meaningful, you could add another name at the beginning.
Ram Peter ka seb khata hai. = Ram eats Peter's apple.
Now coming back to the original sentence.
Peter seb khata hai. = Peter eats an apple.
Peter apna seb khata hai = Peter eats his (own) apple.
No. The है marks the verb खाना as being in the present tense and can't be dropped.
This is similar to how 'is' is used in the present continuous tense in English. Eg: You can't drop the 'is' from 'Peter is eating'.
The only exception is for negative sentences containing नहीं. In that case, है becomes optional. 'पीटर अपना सब नहीं खाता' (Peter doesn't eat his apple) is correct.