The first one is already possible, except fully diminished seventh chords which are currently not supported by Hookpad. This must be indirectly done using borrowed chords, and sometimes copy/pasting across modes, since the explicit way has been precluded.
Further extensions are also rejected, see above. The ♯5 remains in the database after it was disabled.
Inversions of add7 chords (same as seventh chords when no further extensions are allowed, except perhaps dimM7) are possible, so are add9 chords except the inversion that puts the ninth in the bass.
Inversions of sus4 and 7sus4 chords were possible, but disabled in the interface as soon as sus2 was introduced. In particular, inversions of the 7sus2 chord correspond to the add11 chord which, like the augmented fifth embellishment, stays in the database but is no longer interpreted.
Slash chord needs to be implemented, although its usefulness might be limited to the diatonic 11no3no5; Hookpad supports these slash chords generated from borrowing modes, but currently it won’t accept chords like B/C or Fm/E that do not come from the diatonic scale.
The usual way of notating slash chords in Roman numerals is similar to that of applied chords, but with the bass scale degree (often with the ^ mark) instead of the target scale degree. For example, Vno3no511 is the same chord as IV/5.
CM7♭9♯11no5/B = [B C Db E F#] = Bsus4♭2add9 = Bsus42add♭9. By the way, most of the time Hookpad appears confusing to users is not because of chord options (although a lot of applied chords in the database are misleading), but because certain features are mentioned in the manual but not explicitly instructed with text in the editor, e.g. changing octaves, copy/pasting, or adding new rows.
Added sixth, on the other hand, might be added since they often do not represent the first inversion of seventh chords (in the same way that secondary dominants do not represent applied chords so that they are accessed by borrowing modes).