While waiting for the true experts to cover question 4 in more detail, here's my 2 cents: there are significant advantages to specialized planets:

1) Maximize the effect when building an economic / manufacturing / tech capital on that planet

2) Maximize the effect of any buildings that add to manufacturing (e.g. the forges whose name I forgot, any of the "+20/30/...% production to all manufacturing on this planet" buildings) or research (similarly to production, any building giving +25% to all research on that planet such as research coordination centers)

3) Allows for quick production of military ships: it's often better to have 1 ship at turn 3 and another at turn 6, rather than having to wait for 2 ships to become available on turn 6. Speed is key in Gal Civ II, whether it is during the colonization phase or when building up your military.

4) Planets focused on construction will allow you to build galactic wonders more quickly.

One big exception would be when you have bonus tiles, then it's often best to make use of that bonus tile (except for farms) even if you dedicate the rest of that planet to a different purpose.

That being said, it's often good to start with at least 1-3 factories or similar buildings on decent size planets, simply to speed up the construction of other buildings. Later on you can still replace them - or keep them around for when you want to upgrade the buildings on that planet.

To keep your economy afloat, most players will not develop all planets early in the game: they will colonize but leave some blank to avoid being dragged down by construction and maintenance costs. Once there is sufficient population on the planet, you can consider building.
You may also want to leave some low quality planets (e.g. PQ 4-5) alone if you have better quality planets in the same system. Let the AI colonize and develop the planet; later during the game, the influence of your better quality planets will usually "flip" the PQ 4-5 over to your side.