Assuming you have a whale pressure switch for your water system, then its often necessary to adjust if you are using battery power, because the pumps ability to reach the pressure required to trip the pressure switch diminishes as the battery voltage drops. The pressure switches adjustment is easy enough provided you follow the manufacturers instructions.
When it comes to the fridge, it depends on the exact model you have, but most modern caravan fridges need to have a 12v connection to the caravans 12v system to run the fridges control circuit, and it's electronic igniter. If your not connected to the mains power, and you battery is not well charged it can affect the way the fridge (and the water pump) operates. You need to make sure the caravan battery is well charged.
Most fridges (and convector caravan heaters and cookers) do have a thermocouple and it forms part of the appliances flame failure safety system. The t.couple works in conjunction with a solenoid coil and gas shut of plunger inside the gas valve. And they have a superb fail to safe record.
To start the appliance the gas valve needs to be rotated to the ignition position and depressed. This physically opens the gas shut off plunger in the gas valve allowing gas to the burner. During this time the ignitor should be operated to ignite the gas flow. As the flame establishes it should begin to heat the tip of the t.couple, and cause it to generate a current. After typically about 5 to 15 seconds, the t.couple should be producing enough current to energise the gas vales solenoid coil enough to hold the gas shut off plunger open, at which point you can stop pushing in the gas valve, and the gas should remain burning. If the gas extinguishes for any reason as the t.couple is no longer kept hot, it produces less current and eventually (within 30 seconds) the solenoid should deactivate and the gas shut off plunger should close the gas supply safely.
During operation, if the flame extinguishes because of a gust of wind for example, many modern appliances have electronic ignition systems which also and independently detect the lack of flame, and these will often kick in and re-establish a flame before the the flame failure device in the gas valve closes.
If the valve instantly shuts the gas off, there are a number of possible things:-
You have not given the flame long enough to heat up the t.couple,
Or there could be a fault with the gas supply or burner either restricting the gas flow or changing the flame pattern which prevents the t.couple from heating up correctly.
Gas supply is running out,
The t.couple or it's connection to the gas valve might be failing.
If an appliance has worked correctly, but later starts to misbehave, do not be tempted to reposition the thermocouple. The cause of the problem will be something else.p, and probably best left to a fully trained and competent fitter for safety.