-If he will return to US before the old AP expires, that will be fine for him to leave after he files the I-131 for AP renewal application.
If he leaves after submitting the renew application and it gets approved before the old AP expires does he still need to come back to US before the old AP expires
-Not necessary. The principle is that he has to have a valid/approved AP in hand before he leaves and return to US before that AP expires.
or is it ok to stay in Canada (until the new AP expires) because there is no gap between the old and new AP?
-Yes. Because he has the new AP which is approved before he leaves, it does not need to use the old AP.