swój always refers back to the subject, while ich/jej/jego refers to another object. It's both translated with the use of their in English but it has a different meaning. Let's say you want to say he is kissing his girlfriend. If you say on całuje swoją dziewczynę then it literally means he is kissing his own girlfriend, because swoją refers back to the subject, in this case he/on. But if you say on całuje jego dziewczynę then you basically express that he is kissing someone elses (some other male's, hence jego, not jej) girlfriend.
O boże, I finally understand what that swój is standing for. Dziekuję bardzo! :-D
"Oni naprawiają swój związek" also translates to English as "They are repairing their relationship", but you have to be careful who does the their/ich/swój refer to:
"Oni naprawiają swój związek" = some people are repairing the relationship they have.
"Oni naprawiają ich związek" = some people are repairing the relationship of some other people.
Yes, depending what you want to say.
'Oni naprawiają swój związek' - they are repairing their own relationship 'Oni naprawiają ich związek' - they are repairing someone else's relationship
Yes, and no. The better word for connection is połączenie, as in internet conection. Połączenie implies a sort of link. While it mostly implies a physical link (as in pluging a wire into a socket), it can also be used for describing a spiritual link between people. Związek is translated best as relationship or union. So a związek internetowy is an online-relationship, while połączenie internetowe is an internet conection.