What I think I hear from your questions is the act of harmonizing with the melody notes (using a full R-3-5-7 set of chord tones) and moving to the next chord is one process. I see this as being a two step venture. Harmony and movement are two specific items.
I assume you are talking about a melody solo and not a bass line. Aeolian is said to produce a sad mood, I really do not hear sad, I hear minor. Phrygian does have a Middle Eastern mood. So if you want a Middle Eastern mood over the sad mood, be my guest. But, what are you going to play over some of the other chords? Most songs have one mood. Play a different mood over each chord, well, there is a better way of going about this. Namely pick one mood and use that over the entire song. We also need to get into or past walking before we go too far into any other discussion. If you would omit
walking over Gm7 and just say playing over Gm7 most of what I say below could be omitted.
When I create a walking bass line between two chords I use the chord tones of the chord I'm playing over -- and then something to tie the two chords together -- that something is where the walk comes in. Two things in play here 1.) harmony from the chord's tones then 2) something to tie the two chords together. OK what is used to walk into the next chord? A chromatic note above or below the next root note, or the next chord's dominant note because that note wants to move to it's parent's tonic note. Then there are a zillion other things that can be used to move from one chord to the next. Books have been written on this subject. But, like most things if we keep it simple it seems to work out best when we are learning how to walk. The ole Country walk of missing the next root by three frets, then walk to it one fret at a time is a no brainer and normally what I do if I'm walking.
Sometime walking bass lines are looked upon as being any full set of chord tones, i.e. if you have R-3-5-7 in the bass line you are using a walking bass line. I do not see it that way. I see that R-3-5-7 as being every other note in the scale which makes it a shoe in as a great harmonizing chord, but, we have done nothing about walking to the next chord. And it's here you start asking about modes, etc --- So I'm going to take for granted your question deals more with modal than walking.
Your question asks about what to play over a dom7 chord --- To answer your question about using mixolydian over a minor dom 7 chord. I do not play different modes over different chords. Why? I think I've already mentioned that each mode has a mood. If I switch moods three or four times in a song -- normally songs do not change moods that often and is one of the pit falls with newbys to modes. Pick one modal mood, work up a modal vamp that fits that mood and go that way. And with doing that I'm playing either major or minor stuff. If I'm playing minor I use the minor modes, Aeolian, Dorian, Phrygian and Locrian. If I'm playing major I use the major modes, Ionian, Lydian or Mixolydian.
Here is a modal backing track using modal vamps for you to play a mode over.
The one thing we need to understand here is those modal vamps are usually no more than two chords, the tonic and one more chord that has the signature note of the mode, i.e. natural 6 for Dorian, #4 for Lydian, b7 for Mixolydian, b2 for Phrygian and b2 and b5 for Locrian. The vamp drones that signature note - there is no V-I resolution so your modal melody can develop into a modal mood.
I'm going to leave #3 alone and refer you to the following post on how to use modes.
Modal Harmony
Save some time - leave modes to the solo instruments - guitar guys get off on modes, I'm never asked to lay down a modal vamp. It's all tonal - I-IV-V with some ii, iii and vi thrown in. My Country is all major and I-IV-V7, now Praise will use all seven of the chords in a lot of the songs. But, again both of them are tonal there is no modal in anything I do in public. Jazz is played in Dallas and Shreveport, but, not in my neck of the woods.
Good luck.