Yes, that's perfect. You can also say "We did some renovations on my house last week." You could also say "We renovated my house last week," but just saying "renovated" -- instead of "some renovations" -- suggests that you did a lot of work and renovated the entire house. "Some renovations" is better if you just fixed/updated a few things.

Yes, that is fine. It means when we make something old and in poor condition look better and newer.