Well ~actually «Su» can also mean "your" (singular) in a formal conversation, and "their".
● Tu casa → Your house [informal]
● Su casa → His/her/its house
● Su casa → Your house [formal]
● Su casa → Their house
you gave some examples,I will correct them for you:
I am your friend "Soy tu amiga" or "Soy su amiga".
that's te correct way :)
I hope I've helped you.