Why is the 7th chord not diminished? and only b5 not bb7
123456712345671 is a major scale in 2 octaves. You harmonize in 3rds from each scale degree (easy way to think skip every other note). For 7th chords you need 4 notes. So,
1357
2461
3572
4613
5724
6135
7246
These are chords given by scale degrees of the original scale. Now make every first number a new number 1 keeping interval relations. With respect to those as roots the scale degrees become
1357 maj7 chord
1 b3 5 b7 min7 chord
1 b3 5 b7 min7 chord
1 3 5 7 maj7 chord
1 3 5 b7 dom7 chord
1 b3 5 b7 min7 chord
1 b3 b5 b7 half diminished or min7 flat5 chord
Always 2 ways to look at scale degrees. As scale degrees of a scale you are harmonizing but when you construct your chords by harmonizing the scale you analyze the scale degrees within a chord by taking the root note of the chord as new scale degree 1 and compare the notes of the chord to that note as a starting point to get the other degrees (the other set above).
Hope this helps with what you were asking.