Quote Originally Posted by fufaika94 View Post
Why 'своего' and not 'моего' to say "my (friend)" ?
Because you refer back to your own friend. Grammatically speaking, you have a subject, which is I, and then you have a personal pronoun that refers back directly to the subject, I and my are closely connected, don't you think?

Just compare:

Он любил свою жену - That pretty much means that he loved his wife, the person he's married with.

Он любил его жену - In this case that would mean that he loved someone else's wife, a wife of another man, because of "his/его", as его doesn't refer back directly to the subject.

That's pretty much the difference between свой/своя/свои etc and his/her/their etc. We differentiate the use of those to avoid potential confusion.

Just a note, while there is much less confusion when refering back to я with мой, it's still preferable to do that with свой as it sounds more elegant if you will.

Quote Originally Posted by fufaika94 View Post
What I meant was like, 'tell you about myself', 'letting you know about myself'.
In that case say something like: ... и рассказать (немного/a little) о себе.