"The apple belongs to me."
Translation:התפוח שייך לי.
Not really. It is true for English, because English always requires a copula in sentences like "She is smart" or "He is a teacher" and the copula in English is always a form of the verb 'to be'. In languages like Hebrew or Russian, for example, no copula is used in the present tense to connect the subject with the predicate when the latter is espressed by a noun or adjective. By the way, English grammarians always use the terms 'subject' and 'verb' together, where, strictly speaking, they should be talking about 'subject' and 'predicate', given that the verb is a part of speech like a noun, an adverb or an adjective, rather than a function in a sentence.
The gender doesn't matter in this case. "Yesh li" stands for "I have". Otherwise, li stands for "to me" or "for me" as in "give/lend/offer/tell/buy/write me something". Oti corresponds to "me" as a direct object of any transitive verb as in "she can see me", "she likes me" etc.
I was confused about this too, & saw a great explanation in Colloquial Hebrew book. Paraphrasing, If you need the direct object et & a personal pronoun, you combine them together and get oti etc. So if it were otherwise: I saw her. Since her is a specific person you'd need a direct object "et" before her, they get combined, the Hebrew version of a contraction... .אני רואה אותה . We love him
אנחנו אוהבים אותו.
Because שייך requires ל to follow it. English "me" can be translated in several ways in Hebrew: אותי, לי, בי and others and when one learns verbs (or technically an adjective in this case), it is advisable to learn the corresponding preposition that follows it and not question it, because sometimes there is no good reason.
However in this case, if you are familiar with the case system, this would be dative, like in other languages that have the case system.