Should a mechanic know if your car has a lower intake gasket leak or a cracked head or head gasket?

I have had issues with the car since shortly after I purchased it used in 2000. The low coolant light would come on quite often. I had the lower intake gasket replaced in 2001 and it seemed okay. Fast forward to 2011. Low coolant light coming on again and car started running hot. One night I had my son who has special needs with me, and coming over the river bridge it went into the red. I was concerned for our safety so I drove aprox.1 to 2 miles with it in the red till we were in a lighted area. I had a friend take a look and he replaced a hose and filled with coolant. I got the car home and it was still having problems so I took it to a shop. They replaced the lower intake gasket for $600.00 I have had issues with it still overheating, took it back and they replaced the thermostat. Still having problems and I had to pull over another night after going about 3 miles down the road. Friend looked at it and he said the fan didn't seem to be running, turned on ac and the car didn't overheat for the remainder of the drive. I have only driven short distances but have had the temp gauge fluctuate alot with it begining to go into the red numerous times. If I turn off the heater (which takes a long time to warm up) and run the ac it will usually stop the tempature from going to the red. I drop it back off at the shop for a third time because it still was overheating after driving 5 miles, and told them about running the ac seemed to help. He stated he could not duplicate the problem and temp gauge went up to 3/4 mark but no further. Picked my car back up on a Friday and sure enough my car was overheating all weekend. Took it back yesterday and I said lets take a ride. He changed a spark plug because it was missing on # 2. Restarted the car and the engine was not missing. He then bled the air out of a line in two places until coolant came out. Restarted and shortly after engine was missing again and white fog was blowing from the tail pipe. He then informed me it was probably a cracked head and they don't work on engines. I asked if that was the problam initally because I would not have spent 600 to replace the intake gasket if I would have know that the head was cracked. He said you did have coolant in your oil when you 1st brought it in, but that it may have been weak and cracked after. There is really no way to know until it is torn apart and and that they don't work on engines and it would be too expensive to repair. Also, my car has been making a gurgle or bubble nosie after I drive it and park.

Thank you so much for taking the time to review and get back with me!