Sure there's some degree of arbitriness to 7, but I don't think you could reasonably claim it's any less than 7, and 7 is even a number wikipedia throws around. Not that there are only 7, just that there are 7 particularly important ones.

I really just think the 13 the current US flag has looks too busy, but this is the only "American" number I could think of which was less than 13. If you have others I'd love to hear!

Can you say more about the stars? Are you against them being in a circle?

There's not really any way to have them "fill up" the blue while still being in a circle (even if you change their sizes), unless you change the ratio of the blue, which would cause it to deviate from that of the flag itself. Maybe I can cook up a 2:3 version for ya.

As for the size of the stars, again they are in the maximum radius circle which fits in the blue, so can't change their position, and making them any bigger would cause them to touch each other or at least feel cramped.

The stars in a circle in the blue is a classic American design which has been done on the flag before (besty ross, cowpens, etc.).