Strictly, #2 and #4 are more grammatically correct.
BTW, we can say a friend of mine, a friend of his, two friends of hers, but not a friend of my sister's, a door of my house's etc. No 's should be used in these circumstances.
And the sentences would read better if revised as:
2-My sister has five friends. I wrote a letter to one of them who is in England.
4-My house has five doors. I oiled one of them that creaked.