Hm/Ab (Bm/Ab) = 777454

H#7 - нет такого, есть или A#7 или H7

Cmaj7(no5) = C7(no 5) = 01323x

F7M = 0123xx
C/A = 01020x

Dm\F = 132001

Hm7/5 (Bm7/5) = 10101x

Amaj = A = 03330x

Dmaj = D = 2320xx

D4 = Dsus4 = 3320xx
G4 = Gsus4 = 330033

I'm sorry, but the tablature for the chords, is wrong.
I'm not talking about the chords with "*", which is extra check.
But already known chords are described incorrectly.
(from first string to sixth)
A = 022200
Bm = 234422
E = 001221
F#m = 222442
D = 23200x

According to your description, the chords "A*" is "A/D", but again not exactly these chords, because in the chord, the first string should sound.