1. Nope. You can capture the 'independant' extractors that can be found in some uncolonisable grav wells, but you can't build anything in a grav well unless there's a planet and you own it.
2. No, these limits don't change. Each planet type can be upgraded a fixed amount of times in each category - for example, asteroid planets only have one Population upgrade, while terran planets can be upgraded four times.
I can only assume that you mistook a 'greyed out' icon (can't afford it) for a 'maxed out' icon (has a gray 'frame' around it).
Oh, and just for reference, tactical upgrades let you build more defences (turrets, hangars, etc), logistic upgrades let you build more civilian structures (labs, trade ports, etc).
3. There are ships with abilities that can disable either an entire ship, or its phase drive. If a ship is interrupted while phasing, it starts the whole 'fire up the drives' sequence again. As such, you can keep a ship from jumping if you can keep interrupting it. Maybe this is what was happening?
4. The empire tree, on the left of the screen. Learn it and love it.
In the empire tree, the icon of any cap ship that's levelled up will have a small white '+' sign in the corner. Just click the icon to select the ship and assign its points.
(Incidentally, the icon of a flagship will have a bold, upwards pointing white arrow, and the icon of any ship that has unassigned hangar bays will show a smaller white arrow pointing to the right.)
5. Form them into a fleet, or right-click on the 'join fleet' button for each ship, to turn off the 'auto join fleet' behaviour.
6. In general, I'm of the opinion that hangars are the most effective static defence, as their strike craft can reach anywhere in the grav well. Turrets are good for defending orbital structures, but not the entire grav well (or even just the planet).
Build a repair bay, then some hangars around it, and throw in a few turrets to defend them both. Remember that fighters and bombers are effective against different targets, and build a mix of both.
