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A few things worth noting about fuel systems:
1. Fuel pumps use fuel as a lubricant. As you said, you want to avoid any situations where it it not fully submerged. 1/4 tank is a bit conservative though unless Explorers are bad about this (I don't know.) My Civic is good down to about 1/10 tank.
2. Gas tanks accumulate sediment in the bottom over time. The fraction of your tank that is sediment is inversely proportional to the amount of fuel left in the tank. If you let it get too low then you will suck mud through your fuel filter and pump before the engine quits. If you ever "run out of gas", be sure to replace your fuel filter.
3. All fuel storage tanks have some amount of sediment in them proportional to their age. Try to avoid buying gas from a service station the same day it gets topped off from the truck and definitely not if you see the truck filling it up while you're there. The fuel truck stirs up the sediment in the storage tanks and it takes awhile to settle out again. You're paying for gas, not mud, and that stuff will stay with your tank until you get it pumped or change the filter.

Well guys, I got my truck back yesterday. The culprit (Drumroll, please):

Fuel pump.

As I should mention, one time I let my fuel get to almost empty, until I was able to fill it up. That caused the fuel pump to get too hot. Another thing they found was that the fuel filter was actually clogged up pretty good. Also, when they did the fuel pressure test, the results came in at a whopping 5 psi. So, I now have a new fuel pump, new filter, and new lines. And the cost for all of this, including parts, labor, and towing fee is:

$330.

On another good note, with the replacement of the fuel pump, filter, and lines, my "check engine" light has gone away (for now).

But, it does come with a catch. They said I should make sure that my fuel level does not go below 1/4 tank. The reason they said this is because if it goes below that mark, as I said earlier, it will get too hot and it'll, in his words, "lose it's prime" (Not talking about you, @primesuspect ). Basically, the pump needs to be, for lack of a better term, submerged to work properly.

They also gave me a bottle of Lucas fuel treatment to put in the tank to help clean the filter as well as other parts in the engine. They told me to put a bottle in the tank every other fill-up.

Driving it home, I noticed a major improvement in my truck's driving (acceleration, idle, etc.) and I am glad that it is back home.