No, you mean Elefanten som är hans vän. the 'that' in your English sentence is a relative pronoun, so it must be som in Swedish.
Sin is reflexive so that only can be used if you have Han/Hon/Den (respectively a name etc.) as a subject and the object is belonging to him/her/it.
For example: He is kissing his (own) wife - Han kysser sin fru He is kissing his (someone else's) wife - Han kysser hans fru
You can also have a look here: http://www.thelocal.se/blogs/theswedishteacher/2010/03/25/sin-sitt-sina/
en vän, 'a friend' is a more serious thing. en kompis is more like 'a mate', 'a pal', or 'a buddy' – it's more colloquial and refers to a less deep relationship.
I don't think so, that is why there is flickvän and pojkvän to distinguish their genders.