1. He has a house. + He lives in the house.

2. He has a house which he lives in.
3. He has a house to live in.

4. He has a house. + He can live in the house.
5. He has a house which he can live in.
6. He has a house to live in.

(Are they correct? Does #3 or #6 mean #2 or #5?)

Yes, well done.

1-3 are correct; they all mean that he has a house and he lives there.

4-6 are correct; they all mean that he has a house and is able to live there if he wants.

5 and 6 obviously have identical wording, so what each one means would have to come from the sentences around it.

Complete the sentence (in/on)(at/of)

All six sentences are grammatically correct. However, there are some differences in meaning and emphasis.

1. "He has a house. He lives in the house."
This means that he owns a house and currently resides there. The two statements are separate and convey a simple fact.

2. "He has a house which he lives in."
This is a more concise way of expressing the same idea as Sentence 1. The relative pronoun "which" connects the two clauses, indicating that the house he has is the one he lives in.

3. "He has a house to live in."
This sentence suggests that he has a house for the purpose of living in it. It emphasizes the availability of a house for him to reside in, without specifically stating that he currently lives there.

4. "He has a house. He can live in the house."
Similar to Sentence 1, this indicates that he owns a house. The second sentence introduces the possibility or ability for him to live in the house, but it doesn't explicitly state that he currently does.

5. "He has a house which he can live in."
This sentence indicates that he owns a house and has the option to live in it. It shows that he has the ability or permission to reside there if he chooses.

6. "He has a house to live in."
This sentence implies that he has acquired a house specifically with the intention of living in it. It suggests that he plans or intends to reside in the house, but it doesn't necessarily state if he currently does.

In summary, #2 and #5 convey the same meaning, indicating that he owns a house and lives in it, while #3 and #6 suggest that he has a house available for living, but may or may not currently reside there.