Have you checked for fuel delivery issues since car dies while driving? Is the fuel pump operating correctly?And how about the carb? - if the float gets stuck while up there will be an interruption of gas to engine. No gassy, no goey!
Could be a CV joint. Or, a FRONT wheel bearing. Have your mechanic check. I have had wheel bearings go bad but the shop was unable to confirm until the damned thing literally fell apart. I told them MANY times I had a bad wheel bearing. They often don't perform a detailed inspection. Have you looked for twigs caught in the frame? It happens.
If you turn the key off and it wont shut off the heater then there are some interesting things you need to check. The first would be the whole ignition switch. When you shut off the key, the power should stop to that accessory. If that is okay then you need to check the controls for the heater. The issue with no heat is one of a blend door being stuck and this could be the controls again.
if you can get engine started by swapping the relay. it could mean there is a fault in the feed wires for the relay or it could be a damaged relay socket, over time the connections can come weak as the copper becomes weak and temperature changes can make them lose contract. you may be able to make them tight fitting again but do this with the battery disconnected so you don't sort out anything.
Your tempermental starting problem could be the park neutral safety switch . They get worn inside an cause this type problem . Next time it won't start place gear selector into neutral an see if it starts then . The cooling running problem is probably the cooling fan timer module . From the diagram it's hard to say which side the A/C condenser fan is on. The A/C fan has blue with yellow stripe wire in the connector along with a black one . I would also suggest you have a qualified repair shop do a voltage drop test on the starting circuit . How to voltage drop test starter motor circuit