The chords are:
Intro:...E7 l D7 l (walking line A,G,Gb,F,) E7 l D7 E7.
Verses: A7 l D7 l A7 l A7
...........D7 l D7 l A7 l A7
...........E7 l D7 l (walking line) E7 l D7 E7
Try soloing with the A blues scale or the A minor Pentatonic.
Yeah. There isn't much we can do for cleaning up that backing; is like they say..."whatever you record stays there". Is easier to add things like effects and such, than trying to correct errors made at the time of recording.