Welcome to the site. Feel free to ask any questions you might have, there are no stupid questions you know. I'm sure we can come up with a stupid answer or two if you like though.

Also, it is always nice to hear a story about a long lived LUV. My 77 has over 200k documented and who knows how many before that but at least another 100k or so.
MEPR is right on about the probable source to your fuel pump troubles. The fuel pump relay has probably gone out on it. Let me give you a run down of how power gets to the pump, as it does not quite work how you would first expect. This may help you trouble shoot it and make certain you are really not getting power to the pump when you should.
Starting out with the truck off, not running:
Turn key to ON: no power to the pump, no power to coil
Turn key to START: power to the pump via bypass relay, 12v power directly to coil via other bypass relay (the two under that cover)
Engine starts, key sitting at ON: Power to pump via relay, triggered by the spinning alternator (ensures pump quits if engine dies, like in an accident) power to the coil from the same source only going through the resistor on the top of the coil
So that covers it. Motor not running, no 12v at the pump. Key to start powers the pump (likely not happening for you, hence the priming being needed) Motor running, power to the pump again.
So, you might have a problem with the relays or wiring. You could have a problem with the alternator or voltage regulator too though. If you are seeing any other signs of a charging problem, that may be worth looking into. My usual test is park facing a building at night, turn on headlights and heater fan, rev the motor. Lights should get noticably brighter with rise in engine speed, and fan should sound faster as well. If you see/hear no change at all then you are not charging. If you can't tell, it might not be charging well enough. Good luck and keep us posted, I'm sure you'll track it down and get back on the road to 700ka miles in no time.
Oh yeah, to answer #1, that is a seatbelt buzzer. The belt latch has a sensor on it so the buzzer will not fire if you are already belted in, but it usually is so gummed up it no longer works. If you want to kill the noise, unplug the buzzer. It is just under the lip of the dash on the driver's side almost all the way to the left hand side. It looks like a relay and will have a two wire connector plugged into it. I think it even says buzzer right on it. Pull the plug, and it will remain quiet ever more with no ill effects.