The harmonic minor scale, as above, is the same as a natural minor scale, but with a sharp seventh. Beyond that, there is no relation - no intervalic path from natural minor as there is for the church modes. It is the first mode of a different family, and as you say, not a major scale mode.

Yes, you could figure out the other modes of the harmonic minor by following the same logic with intervals, or you could check out a site like this . There may be stuff in the GT lessons, but I've not seen it as yet.

On improving your ear - try working on recognising the intervals, so you can hear one note, and then another and be able to tell how far apart they are - gives you relative pitch so if you know what the first note is, you can figure out the rest.... very useful (to me anyway!). Start with major intervals, then minor before finally going chromatic...

Learning by ear - mimicking phrases and songs etc is also very useful, but the interval recognition will lead to this anyway. You should also be able to identify chord types by sound doing this sort of stuff..