Resource mining starbases add to your racial bonuses, so it doesn't matter if any planets are within range.
Xinathium Hull Plating is a trade good and adds +15% hp to all of your ships (as a racial bonus). The Omega Defense System doubles the hit points of ships in orbit around that specific planet. There may have been one more building that gave hp in some way, but I don't remember.
Tir-Quan Training adds a soldiering bonus to your racial abilities. This means it applies to all of your planets-and, in fact, more than that, as it also applies when you're invading a foreign planet. Planetary Defense can be built on each and every planet (as many as you want, actually, though I rarely see the point beyond a few), and it increases the range of values you get when that specific planet is invaded. You can also increase your roll via more soldiering and more tech (though tech has a lesser effect, a significant tech lead will make a noticeable difference).
In general, if you can build more than one of an item on a planet, it only applies to that specific planet-whereas, if you can't, it doesn't. However, as you can see, there are some exceptions to that rule.
A manufacturing bonus tile doubles the base manufacturing output of anything on the tile. If you put a research building on that tile, its output is 0, and double of 0 is still 0. By the same token, if you put your manufacturing capital on that tile, its production value is 0, and double of 0 is still 0. It merely increases your planet's total production by 33% (in DA) or 50% (in DL). The same goes for putting your technological capital on a research bonus tile, etc. As for your other question, with regards to starbase influence, partial tiles do count, and they do receive the full benefit.
Defenses of an economic starbase? As in, putting weapons/defenses on it? Economic starbases have production assist modules for planets, and trade assist modules (arguably for ships), but they do not have any weapons/defenses assist modules. As such, even if you have a fully decked out economic starbase, a ship in its area of influence will not even have 1 more firepower, or 1 more defense. As for the other half of that question, I'm not entirely sure what you mean. Planets do not have combat like ships do; they just have invasions. So the best answer I can give is that, no, an economic starbase does not increase your soldiering on either a planetary or empire basis, and no, an economic starbase does not increase your planetary defense value, either.
In theory, it could-if it had the modules for it, and the planet in question was in the area of influence. But there are no such modules, at least as of DA, and probably as of TA as well, though I haven't explored it extensively. I would imagine they'd be for a military starbase if they were, but I'm just not seeing it regardless.
-
When it comes to weapons/defenses/engines, I typically grab impulse drive within the first month or so. Sometimes I'll dash straight to warp drive for another +1 speed, but only after I have the techs I feel are necessary to kick out quick colony ships fast enough. After that, I generally don't have much of anything that can fight for a while, although sometimes I'll get particle beam from space weapons to blow up the AI's colony ships (it's just so much FUN).
I used to be exclusively a missile guy (since for most hull sizes missiles are the best damage/space ratio), but having changed my primary alignment to evil from neutral, I now focus more on beam weapons, as the evil-only beam weapon is only ~27% more expensive, in terms of total tech cost, than even the evil-only missile...and to be perfectly honest the evil-only missile SUCKS. Further, beam weapon techs are fairly cheap in general, and the EOL beam weapon tech, doom ray, is by far cheaper (in terms of total cost) than either the missile or the mass driver tree. However, its damage is lower than either the black hole gun or the black hole eruptor, and you can't fit as many of them onto a hull (in most cases).
As far as defenses go, I usually pick up two of them, as I've found in most games, even with 9 AIs, they'll all be of one or possibly two weapon types. There are breakpoints where it's not quite worth your while to go to the next tech in the tree due, as the one you have is good enough, and the one past the one you're looking at would be better, but would simply take too long. In terms of defenses, these tend to be around the 500TP and 1000TP marks (base cost), but those aren't hard and fast rules, either. I'd say if a defense tech takes you more than 3 weeks or so you're probably better off sticking with the old one for the moment, though in some cases an exception can be made if it's the next style of that tech (e.g. droid sentries to pd combo iii).
Hopefully that's been somewhat helpful, but there are as many different ways to do it as there are techs, at least.
