"I am already eating my third pear."
Translation:Jím už třetí hrušku.
I don't know. Maybe shouldn't be as a standalone sentence. It is not impossible, bot not that common.
It does not have to be translated. Czech use these pronouns much less in comparison with English. But your translation is correct.
Sorry-- I am still confused. How do we know whose third pear I am eating? Are we to understand that it is MY third pear because I am eating it, but that it might be anyone else's pear? Perhaps you mean, Vlada, that if it were not mine we would be using Jejich of somesuch possessive pronoun?