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1. My sister's house
2. The house of my sister.
3. A house of my sister's.
Am I right when assuming that the phrase 1 and 2 indicate that my sister owns or lives just in one house whilst the third with double genitive contains the possibility of more houses? – Is there any semantic difference between "my sister's house" and "the house of my sister"?
As Alan Carmack says, only (1) would be in common use, and it doesn't necessarily mean that the sister has only one house. " Your phrase (2), "The house of my sister" sounds weird, possibly archaic, to native English speakers. They would never use it in a sentence like "I'm going over to my sister's house." I can't think of any notable semantic difference between the two phrases, though, and both are grammatical.
Your phrase (3), "A house of my sister's," is indefinite, but it still sounds weird to me. If I needed to indicate that the sister had other houses, I would say "one of my sister's houses."
No, your assumption is incorrect. "My sister" could own or live in more than one house (although she probably wouldn't be living in >1 at the same time) and the term my sister's house could apply to one of several of your sister's houses.
A: I'm going over to my sister's house. B: Which one? The one she's had for 25 years or the one she just bought?
The house of my sister can be used pretty much anywhere that my sister's house can be, except it isn't–that is, it's a rare form that sounds stilted.
A house of my sister's can indicate that your sister has more than one house, but not because of "the (double) genitive" but because of the indefinite article. You can also say The house of my sister's and still be talking about the one house that your sister owns or lives in, or only one of them. You are now in the realm of articles, not possession or "the genitive" (which is a term borrowed from some other language and which only roughly applies to modern English, which has no real case system, as is indicated partially by the fact that we rarely say your phrase 2).
First, you are correct about the first 2 phrases that they imply that she owns only 1 house, and the 3rd one implies that she may or may not have multiple houses.
On your 2nd question, there are some slight differences. For example the first one only implies that she owns one house, she owns it and she lives in it. But the 2nd one could imply that she owns it, but doesn't live in it. the house of my sister (It's of her or from her) Maybe she built it or is trying to sell it for example.
The house of my sister's business.
The house (made) of my sister's own hands.
Those are some of the things number 2 could imply were number 1 would not.
