I don't remember which skill it's linked to, but свой is in the notes somewhere. I don't know if I'm remembering the correct technical name for it, but it's sort of a reflexive possessive. When the person doing the possessing is the same as the subject of the sentence, it's more natural in Russian to use свой than another possessive. Think of it as 'one's own'. And it declined just like мой or твой.
Я люблю свою жену - I love (my own) wife.
Он видит своего брата - he sees (his own) brother.
I believe you can use мой, твой, ваш etc in most circumstances, it's just more natural to use свой.
(Native speakers, please feel free to correct/clarify, I just noticed this question was a week old and figured the OP needed an answer, however imperfect! :))
Not a native Russian speaker, but as a Czech speaker I think you're right. This kind of pronoun exists across the whole slavic family of languages I think. As you say, it's used when the possessor is the subject of the sentence in most case. The other personal pronouns are usually to avoid confusion in a more complex sentence, to make a contrast, etc. I assume this is the same or similar in Russian too.
you're right I'm not sure about special terms, but yeah, свой in many cases ia a synonym for possessive pronouns, that refers to any person, and yeah in such cases we'd rather use свой than мой/ твой/ etc. But if you say smth like "It's mine, take yours" a normal possessive pronoun is used in first case: "Это мое (мой моя), возьми свое (своего свою)", but variant "Это мое (мой моя) возьми твоего (твою)" Is also acceptible and understandable even though ppl would doubtfully use it.
So, What's the difference between: ''Я люблю мою жену," and ''Я люблю свою жену." I already know that there's a huge difference between: ''Он любит свою жену'' and ''Он любит его жену,'' but still I really need to know the difference between the two first examples.
You'd have to use твою or Вашу - the thing to remember about свой and it's derivatives is that it refers back to the subject while agreeing in gender, case and number with the object. You can't use свой to refer to something that belongs to someone besides the subject.
It can also mean "your" or "our".
Basically, it means the thing belonging to the subject of the sentence.
Here, the subject is "I", so it means "my (own)".
If the subject had been "you", it would have meant "your (own)".
If the subject had been "he", it would have meant "his (own)".
And so on.
The nominative masculine and the accusative masculine for inanimate objects are identical, whereas the accusative for animate objects is identical with the genitive. I used nominative and genitive because then there's no confusion over the masculine accusative, which changes depending on whether it's animate or not.
Off the top of my head, I don't remember whether свой is ever used strictly as a nominative form, I was just trying to avoid having to split hairs over animate versus inanimate objects. Clearly failed D: