1. Entertainment centers are what you need to increase approval ratings. (Stock Markets ASAP)

2. Starbases can not move, period. A +1 to speed applies to any of your ships that are in the influence area of the starbase.

3. Not sure what you are talking about here. First, you can not colonize a PQ0 planet - so of course you could never build a farm on one. And the farm techs only increase the max population for any given planet of yours on which a farm is built, nothing more.
Nothing to do with “build a farm on an alien world”, which I assume to mean a world owned by one of the AI.

Interdiction Beam

HyperWarp is the required tech for it.

Some things about farming. I usually never research further than the initial tech on this. What it does is raise the maximum population amount for the given planet. And, as you are noticing, the higher the population, the more your moral takes a hit. Pretty much, any population above 16 is going to cause your moral (on that planet) to plummet. So, the more efficient your farm, the higher your population can go, and the more your moral will tank.

Also, your over-all popularity is based on the average popularity. So lower moral on a single planet will have impact. Particularly if it is a high population planet (more influence).

What has been reccomemded to me before is, don't put a farm down on any planet with a base population cap of 16. Where you DO want to put farms down on are planets where you are focusing on Economy. The higher your population, the more income. So, if you have an "Economic Capital" and several Economy growth buildings, you want a higher population. Because this means more money. Again, be careful and don't go overboard on this.

Another reason that you may want a higher population on a planet is for invasion purposes. The more people you have on a planet, the more soldiers you have to jump to a near by planet occupied by another civ. Also, the higher the population on a world, the more troops you have to repell alien invaders. And the more influence that particular planet exudes (for the purposes of converting neighboring planets).

As far as the Star Base question is concerned, you can build modules that will increase YOUR ship speed through that sphere of influence and decrease enemy ships, again "through that sphere of influence". This a strategy wherein you have a couple of ships posted in the area. As soon as you see enemy ships coming in, you can send your ships after them. Since your ships are faster (due to the increase provided by the Star Base) and your enemy ships are being slowed by that same star base, you can defend a wider area. Throw in some sector scanners and this makes for a fairly decent defense. Keep in mind that, the more star bases you have relative to your logistics, the more expensive they are to build, so build with some restraint.

Influence ones deep in your own territory with no enemy territory around? Hecks yes. Eat those babies up.

Seems that some of your original questions may not have been answered so i'll trrow in what litle i know.

1) You should most definietly build the trade goods for morale boosts. there are about 4 of them. Harmony Crystals is the first i believe. Also, look to mine the yellow resources, they will improve your morale. I usually play with one farm per planet, max population winds up at 13b and no morale structures at all. By the end of the game i can have 80% taxes and still be in the green with morle.

2) Military star bases can not be moved. The +1 speed is for your hip that are in its area of influence.

3)In that description i believe its just refering to any worl as an alien world. It really doesn't "mean" anything. It's just a frm you can build on any of your planets.

Absolutely decomission influence star bases that aren't around enemy planets unless they are in danger of being invaded. There is nothing more satisfying than an enemy invading your planet (which sucks) and having it flip back to your control a couple of turns later. But this is not very easy to gage, so yes. Destroy them.

The Military star bases are a more complex question. Certainly, if it means not being able to make a new star base in the New Frontier, I would say yes. But otherwise, i tend to keep them. This creates a second line of defence against invaders. You never know when the tides might turn. Also, the mere fact that they are star bases, make them High priority targets for the enemy. So they will waste time and effort killing your star bases instead of attacking your planets. That will allow you to shore up your other defenses (at least IMHO).

And if you have a fleet chasing you (through several layers of "Frontier" defense), the warp disruptors will allow the remnants of your damaged first wave to regroup with the fresh second wave and crush the enemy.

The influence of other races has nothing to do with your planets' morale. A plant will flip depending on the influence exerted on it by the other race. If the planet has 100% approval / morale, it can still flip. So raising morale will not prevent it from flipping.

The only way that influence and morale are connected is in population. That is, a higher morale (41%, 75% and 100% thresholds) will grow your population faster and a higher population means more influence for that planet.

Aye, but if you go lower than 21%, you start LOOSING people. So that I think may have been the threshold you should stay above in respect to influence for the inverse reason Yar said about 41%+