1. The option is called "Disable Tech Stealing", therefore, activating it means you can no longer steal techs. Keep in mind, that there are two ways to steal them: through spies (which happens very rarely) and through invasion (quite regularly).

2. You can see it on the minimap on the lower right side. Activate the "ownership" button (middle row, second from the left). The blue circle shown by constructors and starbases are their area of effect.

3. You mean change what you are currently researching? Just click on the "Now researching" tab on the lower left side. This will open the research screen and you can select a different tech to research.

4. The "assign" button lets you choose were the mining base sends its resources. There is, however, a range penalty. The more distant the target planet is, the less resources it gets. This is especially apparent with the first line of mining bases, as even a relatively short distance can reduce the bonus to only 1.

5. Go into the "Civilization Manager" (middle row of buttons, second from the right) and then go to the "Stats & Graphs" tab. You will find it there under "Abilities".

6. Yes, and quite a lot of them, too. Which ones and how many is somewhat dependent on the tech tree, but, in general, you can use this guideline:

Diplomacy and culture techs unlock culture/influence enhancing modules
Trade techs unlock trade enhancing modules
"Xeno Engineering" unlocks a mining module which is a main requirement for all the others
Factory techs unlock production assist modules and mining modules
"Advanced Computing" unlocks an production assist module
Propulsion techs unlock speed assist and slow enemy modules
Weapons and defense techs unlock weapons and defense modules and military assist modules
"Advanced Hulls" unlock the starbase hull repair module
Other hull techs unlock additional weapons modules.
The Terror Star line of techs unlock the modules necessary to construct the Terror Star (think Death Star, but destroying stars instead of planets).

Keep in mind that not all of those techs actually provide access to modules. To find out what each tech provides, right click on it.

There are also some bugs in the StarbaseModules.xml file. This means, that you may not actually able to use all of them, because their requirements have been set wrong. This mostly affects the weapons and military assist modules and is, in part, due to the changes to the tech tree in TotA. The races no longer have access to all weapons, but the unlocked modules still depend on each other. But then, you are better off to use ships to defend your starbases anyhow, as the modules alone are just too weak.

 

Hope that helps. 

So, not just changing the current research project but not researching in that direction at all? In theory? Yes, you can. In practice, however, it's a little bit more difficult, as most techs are quite useful and, as the game progresses, may become needed. But you don't have to research everything in a branch. Just take those techs, that are best suited for your strategy.


Bonuses to your abilities  from techs and buildings (like logistics, economy,etc) will be added to your current ability score. If your current logistics are 6 and you research Basic Logistics, it will be 9. The "Abilities" tab under "Stats & Graphs" in the "Civilization Manager" shows always the current number.

You'll also see your current logistics score as you put together ships to form a fleet.

The cheapest way to defend your starbases from a ship maintenance point of view is to use a swarm of drone-like fighters, assisted by military starbases.  Each ship only needs one cheap weapon.  This makes them very easy to replace if they are lost.  Because you can fit more small ships into a fleet, the effects of ship assist modules really come into play.

However as was mentioned, the prerequisites for each starbase module are not always clear or are broken in some cases. The most sensible thing would be for all the weapons and defence modules on starbases to simply require Battlestations, since then you're guaranteed at least one point of starbase attack in each weapon type before anything else weapon-y goes on.

I'm not sure that influence starbases use your influence ability.  With extreme levels of influence ability, the planets to be influenced are already being influenced by some planet of yours, influence starbases add to that.  The main strength of an influence starbase is packing so much influence into a conveniently placed package, if you have all the modules unlocked that is. Then once a planet becomes yours, it produces influence for you, and you don't need the starbases any more unless there are more nearby planets.