There are a few different questions here.
The first is that yes, after Civil War Spider-Man reverts to his black costume temporarily after Aunt May gets shot. This happens in Amazing Spider-Man issues #549-#543. Right after this arc are the "One More Day" and "Brand New Day" story lines. Spider-Man's costume change to black is accurately reflected in the New Avengers comics as well and reverts back to his traditional costume after the "Back In Black" story line concludes.
Next is the question about Secret Invasion. The Secret Invasion storyline ran through New Avengers issues #38-47. Now as far as Spider-Man, I don't recall any Secret Invasion story line running through the main Amazing Spider-Man title (probably due to the already large status quo shift brought about by Brand New Day). However, there was a 3-issue mini-series that addressed Spider-Man and his involvement in Secret Invasion. It was called Secret Invasion: The Amazing Spider-Man.
The final question deals with Mephisto and the removal of Spider-Man's identity. The plot that runs through the "One More Day" story line is a cross over between the different Spider-Man books at the time. This is the order of reading for "One More Day":
- Amazing Spider-Man #544
- Friendly Neighborhood Spider-Man #24
- The Sensational Spider-Man (vol. 2) #41
- Amazing Spider-Man #545
In order to get the full story you need to read the other two comics that are not part of Amazing Spider-Man. Now the final part of your question deals with Mephisto and the deal Peter and Mary Jane make with him. The deal dissolves Mary Jane and Peter's marriage, saves Aunt May's life, and reverses Peter's public reveal that he is Spider-Man which he makes in Civil War. Although the Avengers do not remember his identity or his marriage, all other status quo's were preserved in the Marvel Universe.
I hope this helps and happy reading!