exactly what the title says, i dunno if this has to do with the other problems that i'm having, but i've had this problem for a while. is it normal for the fuel pump to stay on for like 20 seconds after i shut off the car when the engine is cold?

Not normal. You might have a stuck fuel pump relay. Can't remember if it has constant power to pump or if it's switched on with key. The relay is switched on when the key is on and engine is running. If relay sticks, could possibly run the pump with key off.

Engine cold, oil thick
will keep the oil pressure up
the pump stops when the pressure bleeds down

interesting.

Fuel pump should not be on when ignition is not on. I would lean toward a relay. Switch out the fuel pump relay with the one for the fan(s), and see if problem persists.

The fuel pump oil pressure switch at rear of block.This switch is hot all the time (not keyed ) and operates the pump when OP is over 4psi. If the block is holding oil pressure cold , then it would take longer to come down below the opening point

The pump relay is controlled by the ECM , not the key.The FSM states relay only used for prime and startup.Once OP over 4 psi ,pump runs through OP switch

is the car driving ok?
maybe its something simple like not enough pressure so its stsying on to build it up?

Normal. Shows good oil pressure actually. Not to worry.

Change your oil pressure switch. Had the same problem in one of my cars.

What happens when you start it
when it's warmed up.

This is normal. The oil pressure switch is a "backup" to activate the fuel pump in the event of a fuel relay failure. Cold engine = abnormally high oil pressure, which remains on key-off, which holds the fuel pump on longer.

I can agree with the oil pressure, but I think it could be the relay as a possibility. It may be activated through the ECM, but the contacts can be sticking. ECM just sends power to the relay coil. The contacts come together when the coil is energized. If the contacts are sticking for a little bit, it can keep the fuel pump running. Check the relay first with a fan relay like suggested above. If you still have the same issue, then get a new fuel pressure sender.

How this circuit works, I think: Turn the key on and the ECM energizes the relay, turns on the pump only for a few seconds to build pressure. When you start the engine the ECM gets a RPM signal from the distributor and restarts the pump while the engine is running. When the engine shuts down for any reason and RPM goes to zero the ECM opens the relay. But the failsafe is a separate oil pressure switch that keeps the pump running as long as the engine has oil pressure, key on or off or whatever. Direct circuit. Time the runon after the engine shuts off. If actually 20 seconds as you said it may be you need a new OP switch. If a shorter time and it just seems like 20 seconds, probably all is ok.

Another:

But is wouldn't hurt to check the relay with the fan relay. The ECM only controls the coil side of the relay, not the contact side. Energized or not, the contact area can stick and give the pump power. Not saying it's the only thing that can happen, but is a good possibility. The oil pressure thing makes sense too. I'm just saying to check everything before you throw a part at it that is not needed.

i agree with the oil preasure dioagnosis, mine does the same thing and its normal when its hot. completely normal

Yes, mine does the samething when cold and
normal when warm or hot

My '82 has always done that-totally normal.

well then, thanks for all the responses! haha i mean like i said, i've always had this problem.... and i guess its no big deal, i mean the car drives fine when it has no check engine lights (not like now, freggin code 42)

Should be no big deal