You can have one fleet attack and one fleet defense module take effect per fleet.
The per-ship bonus modules (in influence only, IIRC) factor in additively, though (for instance a Tulon and an Avenger are 20% fleet and 20% ship for a total modifier of 40%, not 1.2x1.2 i.e. 44%). But it's only for that ship, of course-your other ships will still be at a 20% modifier (for instance).
However, while the aggregate fleet numbers don't show any stacking (for instance Zalon + Xalax for 55%), the individual ships within the fleet management screen do, so it's difficult to tell exactly where the mistake is at without testing.
The problem with fighting battles to determine this arises from the fact that not only does luck influence attack rolls but not defense rolls, but that there are rolls in the first place.
In answer to your other question, virtually everything stacks, especially improvements, outside of warp bubbles (which fleets of haste is considered to be).