I know the central yellow power battery (or whatever it's called) is powered by the fear of every sentient being in the universe, or something along those lines (I haven't read any GL comics [yet; I just ordered GL: Rebirth]), but what is an individual yellow lantern's power fueled by? Like, how do they bring their constructs to life? Green lanterns will their constructs to exist. Is this how all lanterns do it? Do yellow lanterns will their constructs to exist too? That wouldn't make any sense. Green is the color of will. So do yellow lanterns bring their constructs to life with their own fear? That doesn't seem right either. Sinestro doesn't strike me as a fearful person. I guess will makes more sense than anything. It has to be something. If there wasn't a specific attribute a lantern's construct is based on, then what limits would there be? Not imagination. It's easy to imagine what you want to create. That's just the part where you envision what you want to happen. What is it that makes that happen?

Yellow Lanterns are recruited on the ability to inspire great fear, just as Green Lanterns are able to overcome great fear (not lack fear, as had been previously indicated). That explains why a lot of Yellow Lanterns are really creepy-crawlies, horrifying guys.

Think of will as the conduit through which constructs are made, regardless of Lantern Corps. Will requires concentration, determination, focus, discipline. In a Justice League story a while back Prometheus stopped Lantern Kyle Rayner with "neural chaff" which messed with his focus. A Lantern unable to focus can't create constructs.

Yellow Lantern rings are powered by individual power batteries that, in turn feed from the Yellow central battery, just like the Green Lanterns.

There is no good answer because it really doesn't make sense. It's a perfect example of how poorly thought out Johns' GL mythos is. It's a lot easier to look at them simply as palette swaps of the Green Lanterns and just forget the whole fear thing.

All rings require will to use. Its just that Green Lanterns and their rings are supposed to rely purely on willpower rather than have their judgement impaired by emotion. Branching off from Will are the six emotions that any sentient being can feel (fear, hope, rage, avarice, love and compassion). Sinestro believed that will alone wasn't powerful enough to bring order to the universe, and that only by adding the emotion of fear could true order be established. So while a Yellow Lantern ring does require willpower to form the construct, the constructs they form are generally shaped to bring fear towards their opponent (for example, constructing what scares their opponent the most) and thus why only people who can instill great fear are members of the Sinestro Corps.

In older continuity it was stated that Sinestro's yellow ring (and later Guy Gardner's) was recharged by stealing the power of Green Lantern rings (or possibly tapping to Parallax who was trapped in the central battery at the time through the ring). Since the formation of the Sinestro Corps the rings are recharged by using Yellow Power Lanterns and connecting back to the Yellow Central Battery just like the Green Lantern Corps does.

The only Corps that do not require a central power battery or have a set power charge are the Black and White rings. Black rings are charged by taking life and White rings are charged by experiencing life.

One of the things that is confusing about the emotional electromagnetic spectrum is how the six emotions (I will never consider Will an emotion just as Death and Life aren't but acknowledge that without Will the other emotions wouldn't exist) interact with each other. For decades its always been that fear is the opposite of will. That was when yellow and green were the only two colors. Now that we have others I think DC needs to re-invent the breakdown of the emotional spectrum a bit more. My thinking of the spectrum would be:

Avarice (Orange) - Rage (Red) - Fear (Yellow) - Will (Green) - Hope (Blue) - Love (Violet) - Compassion (Indigo)

where

Fear and Hope are opposite (with Fear weakening Will and Hope strengthening it)

Rage and Love are opposite (with Rage clouding it and Love focusing it......also both of them require a transformation by their bearer with Red Lanterns losing their hearts and Star Sapphires being encased in crystal for a bit)

Avarice and Compassion are opposite (each completely subjugating will to its own decree)

Technically Hope weakening/canceling Fear has been brought up before as well as Hope un-clouding a Red Lantern but these dualities are a good start to understanding how the emotional spectrum works.

Yes, I understand clearly now. Your reinvention of the emotional spectrum also sounds promising, although I wouldn't say "love focuses". lol. I also personally am not into the whole "fear weakens will" thing. If you think about it, fear strengthens will. It causes adrenaline to pump into your veins, heightening your senses and making you quicker to react. Fight or flight. It does cloud judgement, since it makes you paranoid, but doesn't really cloud will.

If you start logical deconstruction here the whole lantern corps concept kind of starts to fall apart

Yeah, but it's fun to dissect things