Can you use other Apple Watch Bands on the Series 7 watch

Yes and they should fit as they did on another watch.

Any band which is 38 - 40mm will fit the new 41mm watch

Any band which is 42 - 44mm will fit the new 45mm watch.

And they will fit perfectly as I just moved up to Apple Watch 7 and all of my bands which fit my Apple Watch 4 fit exactly the same.

You're welcome. There was a rumor long before Apple Watch 7 as released that previous bands would not fit the new watch. And you see how rumors go........it wasn't true at all. A lot of people have significant investments in Apple Bands. Me for one! I'd be very upset if all of the sudden my bands didn't fit anymore.

Yes. They won't fit perfectly, but they will work just fine.

How do I know which size I need?

Which size Apple Watch did you buy? There are only two. The small is 41mm. The large is 45mm.

Exactly. I have hundreds of dollars invested in higher quality bands for my Apple Watch now.