My dash lights don't work and my heater and sunroof stop and start working at the same time on 2001 dodge stratus 4 door

Does the engine reach normal operating temp? Are the heater hoses hot? If that checks out, maybe a temp door, under the dash has a problem?

google recalls for year make model. there are numerous recalls on electrical problems. dealer will repair for free.

Used to be vacuum controlled, but now the doors inside the heater/AC suitcase (housing under the dash for the heater and a/c unit) are electrical rheostat controlled, and tend to give problems. These rheostats open and close the doors used to control where hot air and cold air is tunneled to the dash vents. (the hot to cold dial on the dash is a rheostat which controls an electric motor connected to a door, which opens for hot air, and closes for cold air). The rheostat or motor, it controls, has gone bad. Find an independent garage that you like, (NOT the stealership) and the price to fix will be a lot cheaper and more reliable. Good Luck

when jump starting volvos turn the lights on this will stop the power surge from blowing fuses or relays that have stopped all your bits from working

there is a fuse holder that is yellow under the hood on the 2001 stratus r/t. you have to pull the yellow holder up, not out, to remove the fuses. both are 10 amp. then you can remove them. if you have a tester, you can test them first. they go to upper part of the dash, interior and moon roof. I am a mechinac and had to troble shoot this problem. an easy fix.

How was the heater core verified ?

There is limited information in your description. I would only be able to guess at this point it may be the fuel pump.
How long does it run before stopping?
When you say stop you are refering to the engine going off - right?
Was the car parked/stored for a long time?
Is this evertine you start it or only at certain times, e.g. cold morning, after a long drive re start.
Does it make any specific sound before it shuts off?
Do any of the dash lights come on just before it stops?
Does it re start again just after it has stopped - and how hard is it to restart?
When was it last refueld compared to when the problem started?
Was anything done to the car just before it started to show these symtoms

Replace the Blower Motor Resistor.It will be located in or near Blower motor box.

Alternator

check or have someone check the dash console where the knobs are i've had to replace mine once and maybe twice now