Most RV refrigerators have no motors, when running on electric they run a heating element not a motor.

Gas/electric refrigerators operate on the absorption principle. This is a relatively simple method of cooling which uses no moving parts. The cooling unit, which is the maze of tubing you see at the rear of your refrigerator, is where the work is done. The cooling unit is charged with ammonia, hydrogen, water, and sodium chromate. In a short simple description of the cooling process, the ammonia is liquefied and flows into the hydrogen gas in the evaporator (freezer) where it evaporates rapidly, this is what causes the cooling.

If you were trying to use it on electric as most people do, you probably were experiencing low voltage. Which is common in campgrounds, especially at the times when they are filled to capacity. The simplest fix is to switch to gas operation until the crowd goes home.

RV refrigerators depend on a specific amount of heat to operate properly. On electric most are designed to operate within a voltage range of +/- 10% or 108 to 132 volts assuming a 120 volt nominal rating. At 108 volts you are getting only 90% of your needed power ( I have seen voltages as low as 90), add that to a hot humid day and you're going to have some cooling problems.

Since you are operating a heating element and not a motor low voltage should not damage your unit, it just will not work as efficiently as it was designed.

High voltage, up to the design limit shouldn't normally hurt the refrigerator either, although it may shorten the life of the heating element and if over the design voltage can damage the cooling unit from overheating. This is particularly true of older units, newer models have some limited protection from overheating designed into the cooling unit.

See the above about electric. If properly adjusted and vented gas is a more stable heat source.

Yes, you must level your refrigerator. When parked it should be level in all directions +/- 2 degrees, which is approximately a half bubble off. The absorption cooling process relies on heat and gravity to move the coolant around, when moving on the road the motion will help prevent the coolant from pooling in the boiler and overheating. It is this overheating of the coolant that contributes to cooling unit failure.

Twenty some years ago when I first started in this business, that was the first thing we tried when a refrigerator quit working. Sometimes it helped, most times it didn't. What most people mean by burping is removing the refrigerator from the unit and turning it upside down for a while then retrying it to see if it works. If it works it usually means that you had something floating in the unit which blocked a tube and the inversion process cleared it. This is usually only temporary. Most manufacturers and technicians have given up on this process. Although it may be interesting to note that at least one manufacturer even had a specific pattern for turning the refrigerator upside down.

If you are doing this yourself and not paying someone to do it, you have nothing to lose but some time and occasionally it works. But most refrigerators take at least an hour to remove and reinstall if everything goes right, so, if your going to pay for this service you may want to reconsider.

If your refrigerator doesn't work on either gas or electric and it has been verified that those systems are working, then the cooling unit is all that is left. The cooling unit is the actual working part of the refrigerator and aside from the cabinet it is the single largest part of your refrigerator.

Changing a cooling unit entails removing the refrigerator from the coach. Then dismantling as much of the refrigerator as necessary to remove the unit and reinstall the new one. The amount of work involved varies with the different models and brands. So it depends on your skill and abilities. It also requires at least 2 people for the removal and reinstallation into the coach.
It is also up to you to do all the necessary testing, including checking for gas leaks, and verifying that the installation area in the coach is setup properly.

This could be any of several things, but, one of the easiest for you to check is the venting. The vent at the back of the refrigerator and the roof vent must be clear. This means no furnace filters or screens on the lower door vent, and the roof vent should have a coarse screen on it under the cap.