Well, let's see. Did the Ferengi have FTL sensors? Yes, it must have in order for them to lie in wait at a moon, spot the Stargazer traveling by at Warp 2 and then catch up and attack it.
Not necessarily. It's a bit more likely that Stargazer dropped out of warp for a moment -- for whatever reason Picard didn't bother to mention -- and the Ferengi ship dropped out of warp at point blank range and opened fire. That would be somewhat consistent with the Ferengi lying in wait to ambush the first passing ship that happened by, especially if Stargazer's deceleration point was something they could predict ahead of time (after all, how many deep moon craters just happen to be perfectly positioned in a solar system where a passing ship will fly over them at warp speed?)
Probably had something to do with what Stargazer was doing in the system in the first place, and why she originally stopped.
And what was required of the Picard Maneuver?
1. High Warp
2. The Enemy choosing the wrong target to fire at.
3. Possibly some kind of timing for a sensor bearing "return arc".
The wrong choice doesn't seem all that relevant, it's just something Riker happens to find really amusing. Data even says, later, that there is no known counter to the Picard Maneuver, which implicitly rules out "just fire at the closer image." The logical conclusion is that the maneuver works the way it does because theoretically you don't have time to fire on EITHER image before your attacker cripples you, in which case it was the Ferengi's last spiteful shot -- as their ship was exploding around them -- that was aimed at the wrong target.
How does "seem to disappear" fit into this?
It's what Data says later in the episode when Stargazer tries it on the Enterprise. The clear implication is that under normal circumstances you cannot track a starship moving towards you at high warp speed.
The main viewer does show that the E-D had no problem tracking the hop though.
AFTER Data reprogrammed the sensors to scan for a gas compression and focus their attention on that. Under normal circumstances, there'd probably just be a flash of light as the second Stargazer image suddenly appeared and opened fire.
And again, the issue is that the sensors won't detect Stargazer's new position until it drops back to sublight speed. The whole while it's at warp, it appears to still be sitting in its original position, not moving at all. Scanning for a sudden compression of gases gives those sensors just enough warning -- milliseconds, really -- of where stargazer is about to be.
Something else to consider here is that Picard's account of the battle implies a lot of warp maneuvering is going on her, with some sudden stops and starts as ships jump in and out of firing position. Stargazer either stops or is forced out of warp by the Ferengi, but it's just as evident that the Ferengi conclude their first attack by jumping to warp and flying to the edge of Stargazer's sensor range, then returning and coming in for a second, very sudden attack. They do this again, sweep out to a far out position, but this time Picard uses their own trick against them and jumps into their face at warp speed, hammering them before they can respond. In this case, that would support the idea that their "firing on the wrong target" was a misplaced parting shot from an already defeated foe and is otherwise the only reason Picard survived to tell the tale. But it also emphasizes the point that neither vessel can fully track the other at warp speed: one way or the other, they can only shoot at each other if their relative velocities are sublight, and warp strafing a la TOS is out of the question.
I could see one other possibility, though: it could be possible -- after a fashion -- to track a vessel that is moving AWAY from you or even perpendicular to you at warp using only STL sensors. The image would be highly distorted and its exact location would be unknowable, but determining its course and speed would be pretty straightforward. You couldn't track it, exactly, but you could FOLLOW it, and with that possibility, the need for FTL sensors in TNG utterly disappears: even the listening posts that seem to be tracking approaching starships at warp speed could just as easily be conventional telescopes or sensor mounts placed at strategic positions that can sound the alarm if anything flies past them at warp speed.