We do know a few things for certain:
1) The Enterprise-D saucer has warp coils. To the amazement and relief of everyone, they are of sufficient quality that they can sustain Warp 9.6 for at least one brief shining moment.
2) A matter-antimatter reactor is not a requirement for warp travel.
3) Without constant power to maintain a warp field, warp fields naturally decay or even suddenly collapse.
4) Glowing bits are not necessary for warp (although they are often an indicator of warp). See the original Enterprise as the prime example.
The blue glow on the nacelles seem to be a way for the ship to cool off because thermodynamics, not necessarily an indication of warp. In the TMP movies, they start glowing blue when they go to warp because that's when the warp core kicks into high gear. Presumably, the Enterprise-D is always generating huge amounts of power, so the nacelles are always glowing. When it goes into warp, the nacelles flash because of the sudden jump in power output.
How can we reconcile "Encounter at Farpoint", "Arsenal of Freedom", and "Brothers"?
I'm going to say that the Enterprise-D saucer has warp capability (it has warp coils, and it has the ability to generate power), but it's a crappy warp drive that requires a lot of work by the crew to make it work due to the saucer's geometry.
Why is it a risk to separate the saucer at high warp if it's automated? Generating and maintaining a warp field must take a lot of work by an engineering crew on the saucer to keep it from suddenly slowing to Warp 2 in front of the engineering hull that is going at Warp 9.6.
Why would LaForge send his chief engineer to the saucer? Because he was about to separate the saucer at warp, suddenly got cold feet (what would Starfleet do to a junior officer who wrecked a brand new Galaxy-class starship... assuming he survived?), and then decided to separate while the ship was stationary. His chief engineer would be the most qualified person at the moment to lead his crew in getting the saucer to warp speed and dealing with its finicky ready-to-collapse-at-any-moment warp field.
Why would Picard expect the separated saucer to drop out of warp in two minutes? Because Data is only one person (even if he is quite the one person), not a whole engineering team. The saucer's warp field is going to fall apart without a number of people fiddling with it. It's like the Enterprise in TSFS. She's just not the same with a skeleton crew.