Sounds right to me. The tricky thing with 7th chords is they use the dominant 7th...chords that use the major 7th are called major 7th chords. I think of the dominant 7th as the flatted major 7th.

13th chords are in the family of extended chords (9th, 11th, 13th). You form these by making a 7th chord (dominant 7th) and adding the extension...which like you said is coming wrapping around or going back to the beginning of the scale...up an octave. A 9th is a 2nd, which would make an 11th a 4th and a 13th a 6th.

Interesting that this topic would come up today since just yesterday I was reading up on what make a G2 chord vs. a G9 chord. To me it was confusing since the 9th is just an octave of the 2nd. The main difference is the G9 is based off a 7th G chord.

Things like "add 9" chords I think just do that...take the base chord and add a 9th note.

There may be some sublties I missed here...not pretending to be an expert, but this is what I read recently. Perhaps it's starting to stick :).

More reading....

According to wikipedia, it looks like extended chords are based on their previous extension....so 9th chords are based on 7th chords, 11th chords are based on 9th chords, and 13th chords are based on 11th chords.

So a 13th chord would have root, 3rd, 5th, 7th, 9th, 11th, and 13th. The 11th and 9th can be left out.

You learn something new every day :).