A-7b5= A C Eb G
Adim7= A C Eb Gb (think of it as taking a dominant 7th chord and raising the root a half step)
ex; Ab7= Ab C Eb Gb
Harmonizing- the melody note does not have to be the root of the chord, nor a chord tone. These are good places to start though, but the melody could be the 9th, 11th, 13th, etc... there are no rules hear, you must try to figure out what you are hearing in your head, and then through trial and error try to affix the appropiate chord that gives the results you are looking for.
hint; try to think colors when assingin chords to melodies. Do you want this particular section to be dark (minor) or bright (major) bluesy (dominant) tense (diminished, augmented) etc...be creative. Look at other peoples charts for inspiration, Pat Metheny does some very interesting compositions. Good luck!