Pump runs for a few minutes becomes hot and stops then starts again

check adjust belt tension
may have to clean under belt area as there could be a build up that is stopping the free movement of the belt as it gets hot

Could be a bad electrical connection or if the pump is running really hot due to being tight , blocked or mechanical failure, it may be overheating and cutting out. When it cools down, it will try to start again. Check that there is no foreign objects stuck in it such as hair, lint etc.

Sounds like an electronic fault. It could be bad solder joint if the turntable has had a recent impact or fall. Otherwise I would suspect a semi-conductor with a thermal problem - getting hot when it shouldn't. Check with your finger for hot parts! Don't burn yourself. If you find one spray with Servisol Freezer Spray. If the instant cool starts it working you have found the faulty part. If it doesn't then it's back to the drawing board!

Fan bushings are shot. Replace blower motor

If the engine has a black pump on the side of the engine it may be faulty, there is a diaphram inside, but the pump is non servicable, it takes a pulse from the cylinder head or rocker box, this pulses the diaphram, which then pumps the fuel, as there is no gravity feed from the tank, it requires the pump to fill the carb.

Your ignition coil is failing when it gets hot.make sure the cooling fins on the flywheel are not plugged up.you will probably have to replace the coil.

This sounds like overheating. These small generators don't have overheating protection, but if a low oil pressure or low oil level is present it may be the reason for stopping.

Check the oil level in the starting conditions and again when it stops. It may become under the "stop" level and after some time the precipitated oil has reached the "start" level. The same may be with oil viscosity and oil pressure.

Try to add some oil or change the oil with bigger viscosity.

change the fuel pump, is bad,

Sounds like your motor is overheating, This is a sign of windings going bad and sorry to say you will probally have to replace the motor.

It sounds as if you have a defective drive motor.  After the motor runs for a while and heats up, the internal thermal switch cuts it off before it gets too hot and becomes a hazard.  Once the motor cools down and the thermal switch makes up again, it will run and then repeat this process.