#1
The song in question is "Lords of Karma" by Joe Satriani.

The first two chords are:

A5(#11)     | A13sus4
-11-----------|-5
-10-----------|-7
-9------------|-7
-7------------|-5
-0------------|-0
---------------|--

(obviously, A Lydian and A Mixolydian)

Now, those two repeat for the Verse and Solo, just for context. Now, the part immediately following the solo is what I'm talking about...it uses these chords (arpeggiated, not strummed):
(also note, all chord names are from tabbook >_>

1. G7add4(13)
-0
-1
-4
-3
--
-3

2. Ab(#11)
-
-5
-3
-
-6
-4

3. Am(b13)
-8
-6
-9
-7
-0
-

4. Fmaj7/13
-0
-3
-2
-
-
-1


5. G7add4(13)

6. Bbmaj13b5
-5
-5
-7
-5
-
-6

7. Am9
-
-6
-9
-7
-0
-

8. G13sus4
-8
-6
-9
-
-
-3

9. Fmaj7/13

10. E7
-
-3
-1
-
-
-0


And then it returns to the verse chords. Yeah, sorry the post is so big, and sorry if it looks confusing, but any help would be extremely helpful, because I love the song and those chords form a fantastic melody, but I can't for the life of me figure out how he could've written it...


The tab, if it helps:
   

A5(#11)                              A13sus4
 E E E  E  +H        +W           E E E E +H       +W
||--------11-(11)----|-(11)--------|-------5-(5)----|-(5)-----||
||o-------10-(10)----|-(10)--------|-------7-(7)----|-(7)----o||
||------9------------|-------------|-----7----------|---------||
||----7--------------|-------------|---5------------|---------||
||o-0----------------|-------------|-0--------------|--------o||
||-------------------|-------------|----------------|---------||



 G7add4(13)                                Ab(#11)
                                 ~~~
  Q   E   E  +E   Q.      H      H       Q   E   E  +E   Q    E
|----------------------|--0------------|-------------------------|
|-----------------1----|---------1-----|-----------------3-------|
|---------4--(4)-------|---------------|---------5--(5)-------5--|
|-----3----------------|---------------|-------------------------|
|----------------------|---------------|-----6-------------------|
|-3--(3)-(3)-(3)-(3)---|-(3)----(3)----|-4--(4)-(4)-(4)-(4)--(4)-|

             Am(b13)
  +W           Q   E   E  +E   Q.      Q.    E  +E   Q.
|------------|----------------------|--8------------------|
|------------|-----------------6----|--------6--(6)-------|
|-(5)--------|---------9--(9)-------|----------------9----|
|------------|-----7----------------|---------------------|
|------------|-0--(0)-(0)-(0)-(0)---|-(0)---(0)-(0)-(0)---|
|-(4)--------|----------------------|---------------------|

Fmaj7/13                               G7add4(13)
  Q   E   E  +E   Q    E    +W           Q   E   E  +E   Q.
|-----------------0-------|------------|----------------------|
|---------3--(3)-------3--|-(3)--------|-----------------1----|
|-----2-------------------|------------|---------4--(4)-------|
|-------------------------|------------|-----3----------------|
|-------------------------|------------|----------------------|
|-1--(1)-(1)-(1)-(1)--(1)-|-(1)--------|-3--(3)-(3)-(3)-(3)---|


                 Bbmaj13b5
   H     a H      Q   E   E  +E   Q    E    +W
|--0-----0s3----|---------5--(5)----------|--------|
|---------------|-----------------5-------|--------|
|---------------|----------------------7--|-(7)----|
|---------------|-----5-------------------|--------|
|---------------|-------------------------|--------|
|-(3)-----------|-6--(6)-(6)-(6)-(6)--(6)-|-(6)----|

Am9                     G12sus4
  Q   E   E  +E   Q.     Q.    E  +E   Q.
|----------------------|-8------------------|
|-----------------6----|-------6--(6)--5----|
|---------9--(9)-------|--------------------|
|-----7----------------|--------------------|
|-0--(0)-(0)-(0)-(0)---|--------------------|
|----------------------|-3----(3)-(3)-(3)---|

Fmaj7(13)              E7
  Q   E   E  +E   Q.     W          +W
|-----------------0----|----------|--------||
|---------3--(3)-------|-3--------|-(3)----||
|-----2----------------|-1--------|-(1)----||
|----------------------|----------|--------||
|----------------------|----------|--------||
|-1--(1)-(1)-(1)-(1)---|-0--------|-(0)----||
#2
Well first, if you exclude the Bb and Ab, you've got basic extended chords from C major.

Then, we see that Bbmaj7 is the IV of F, which is a pretty basic borrowing (you'd want to just flat the B over the duration of the chord)

The #11 on the Ab implies the IV, so we would assume it's borrowed from Eb, which could also be c-, so it's borrowing from the parallel minor key - add three flats (or just move whichever scale shape you're using three frets up for a bit.)

V/vi on that E7 if you didn't know - E phrygian dominant should do nicely.

As to learning all those cool voicings - that's experience, really.