A: 3rds and 4th together in the same chord is not prohibited, just not a great sound. Sometimes minor 2nds together in a chord sound better than others, like between the 7th and root in a maj7 chord or between the #11 and 5th in a maj7#11 chord. Even between the 3rd and #9 in a 7#9 chord. So why not in a sus chord? Because:
- It throws the nature of the chord into question. In a maj7 chord the B and C notes are important to the nature of the chord (the chord sounds crappy with the 7th as the bass note but eliminating either, would change it from what it is), same with the #11 and 5 in a maj7#11 chord. A 7#9 chord without both the major 3rd and #9th would turn the chord into something else. But the 3rd and 4th in a dominant chord are conflicting to the nature of the chord. It makes the ear wonder if something is wrong and confuses us.
- It isn’t necessary. The 4th is way more important in a sus chord and there are better notes to add to the chord than a 3rd.
Q: C-E-G-B-D-F-A (maj13 chord) = also impossible? Why? For the same reason, the 3rd and 4th can't be included together in the same chord? But is the 11th note is necessary for the 13th chord?
A: No, theoretically the only notes that must be included in a 13 chord (major or minor) is the 1-3-5-7 and 13. 9ths and 11ths are options. But the general rule is that the 11th, if you were to include it should be raised, as in C-E-G-B-D-F#-A. But once again, they are options and regardless, you couldn’t play a 7 note chord on the guitar. If you were playing with a bassist, you could technically just play the 3rd, 7th and 13th.