Hm... good question. I don't know the rule, to be honest I don't even know if there is a rule, but I'll try to explain it the way I feel is correct. In Dal's dictionary it says "свой" is a possessive pronoun used instead of "мой", "твой", "его", "наш" etc. What you need to know about the word "свой" is that literally it means "my own/your own/his own etc. as opposed to the word "чужой" (which means "someone else's). That is why "свой" is often used for emphasis. In your sentence "У него есть свой дом" you literally mean "He has his own house" (i.e. he is not living in someone else's house, he has his own one). If someone was teaching you how to say your name, you could respond with "Эй, я знаю свое (собственное) имя" which means "Hey, I know my own name" (emphasis again). "Свой" is often used instead of "мой", "твой", "его", "наш" etc. I don't know when you use which, but "свой" is more frequent. My personal guess is that "мой", "твой", "его", "наш" etc. are used when attributing the subject, and "свой" usually attributes the object (or modifiers). For example, we say "Моя мама - учительница"/"My mom is a teacher", but "Я люблю свою маму"/"I love my mom". "Я люблю мою маму" is also possible, but it sounds childish (a child could say that, they actually do quite often). It is also correct to say "Он живет со своими родителями" ("He lives with his parents"). I hope this helps.

Брата зовут Никита, а его сестру зовут Алена. It is gonna be a mistake, using свой. In this case use его\ее\их and other pronouns of this class( I suppose u already know them) And about your frist question. U are right, it is incorrect to say Своя мама. Свой is for inanimate nouns. In the most of the cases. But it is possible to use it with a doctor, man. It is gonna be idioma. In this case Свой=хороший, u can trust this person.

I think the explanation of свой in the function of indicating smb's property is now clear ('one's own'). As for distinguishing мой/его etc and свой, the important thing is that cвой is not used when the belonging is not clear, when you can't say whose object it is (no owner or there are several people mentioned): Это мой / твой / его брат. (свой is never used in Nominative!) Это мой друг и его сестра. Я люблю его сестру. (I love my friend's sister) Это мой друг и моя сестра. Я люблю свою сестру. (I love my own sister) When the subject of the sentence is clearly stated, you can use свой to designate his belongings, because the possession is implied: Где моя шапка (no person - no свой)? Куда Я положил свою шапку? БРАТ ищет свою шапку. СЕСТРА ищет своё пальто.

"свой" is used when you talking about another person's feelings/action to his family members. he loves his sister (он любит свою сестру) but when you talking about your or somebody else feelings/action/discussion to family members of this person "свой" shouldn't be used. we saw his sister (мы видели его сестру) or when you discussing some facts (without any relation) his sister's name is Alena (его сестру зовут Алена) my mom is a teacher (моя мама - учительница) when discussing your family members "свой" shouldn't be used to avoid mistakes. sorry for my bad english, hope this answer will be helpful

So, свой = my own. Я люблю свою машину/собаку = I love my own car/dog. Look at свой as an adjective.