The first time when I was driving was at driving school.
To me, using that instead of when sounds a bit better:
The first time that I was driving was at driving school.
"When" clauses are often used to set up background information for a full later sentence - i.e. When I was young, I was learning to drive ... so it could lead the listener/speaker to be waiting for more from the sentence sometimes.
When I was young 20 years old I was first driving.
You just need commas here: When I was young, 20 years old, I was first driving.
You could also omit "young" entirely - When I was 20 years old, I was first driving - most people would understand 20 years old to be pretty young.
When I saw the matrix that was my last movie
You should say: The last movie I saw was the Matrix.
When you say "X was my last movie" like that, you could be implying you are never going to see a movie again in your life, though the listener/reader could figure out you don't mean that from the context.
When I went to china that was my last honeymoon trip.
Probably you should say: I went to China for my honeymoon
Or: I went to China for my second honeymoon
Saying "last honeymoon" in the manner you did sort of makes it seem like you go on honeymoons all the time, or that you have several memorable honeymoons and you're trying to emphasize that this one is special because you went to China.