Your answer for V7 is perfectly fine, the bottom row doesn’t contradict it, it just has additional information: namely, that if a 9th is added to the harmony it would be a minor ninth. (Actually, I think I probably wouldn’t call it ♭9, since that would imply an alteration of the ninth, but no one anywhere would misunderstand it, so it’s a moot point.)
However, if you’re trying to make a chart that strictly follows harmonic minor, then vii m7(♭5) is incorrect. The vii chord would actually be fully diminished: vii°7. The symbol m7(♭5) is another way of writing a half-diminished seventh chord—sometimes indicated with a diminished sign with a slash through it: viiø7. viiø7 happens diatonically in major keys or if you’re adhering strictly to melodic minor, but harmonic minor would make it fully diminished.
A couple of other adjacent points brought up by your question:
First, your intuition that it doesn’t matter which specific harmonic minor scale you’re talking about is 100% correct. The V7 is a dominant seventh chord diatonically in any harmonic minor situation, and the vii°7 is fully diminished in any harmonic minor situation.
The usefulness of thinking in terms of pure harmonic (or natural, or melodic) minor depends a great deal on the kind of music you’re talking about. If you’re trying to grasp the modal use of these scales in a rock/pop context, it’s somewhat helpful, but in most rock/pop styles the qualities of the chords don’t tend to stay exclusively diatonic, it’s only the harmonic roots that tend to reflect the mode. If you’re talking about Classical music, it’s not very helpful at all, because the the three forms of the minor scale are just an abstraction to help people understand the complexities of minor keys. A piano sonata by Mozart, for example, would never be in C harmonic minor, or C natural minor. It would just be C minor. The sixth and the seventh scale degrees would vary depending on use: the sixth scale degree will tend to be raised in ascending melodic lines (hence the name “melodic minor” for the scale that has a raised sixth going up). The harmonies will tend to have lowered sixth scale degrees but raised seventh scale degrees (hence the term “harmonic minor” for the scale with ♭6 and ♯7). However these are only tendencies, alterations abound.