Power source for fridge whist travelling?

Battery, we never travel with the gas on.

Neither, it should be powered via the vehicle battery when the engine is running.

Battery. I wouldn't have thought it would be a good idea to travel in a vehicle with a naked flame just in case of accidents ..... whether you were directly involved or not. 

If its an absorption fridge, wont it run off the alternator when driving rather than the habitation batteries like it does on a caravan? 

You should not have the option or possibility to run the fridge from the habitation batteries.

When 12v is selected a relay will operate diverting power from the engine's alternator direct to the fridge, but only when the engine is running.

Your owners manual should make this clear.

See page 8 of your Quickstart manual which gives you the same info that I posted above:

https://orbit.brightbox.com/v1/acc-jqzwj/Swift-Group/handbooks/pdfs/000/000/258/original/2017-Swift-Group-Quick-Start-Guide-web.pdf?1472743633 

yes, when the 'battery' is selected on the fridge when driving, its the vehicle alternator that supplies the power. it also charges your vehicle and leisure batteries.

We have a built-in LPG tank and I read that Truma now have a cut-off valve so that gas could be used on the move, however, my dealer was definite that you cannot travel and use gas heating etc. If you have cylinders you certainly should switch the gas off before setting off

I ponder that on some cylinders that have clip-on connectors, 13Kg Calor and Gaslight to name but two. No actual facility to positively turn off the gas at the cylinder.

Our van has an under-slung tank. It also has an electrical gas isolator which shuts off the gas supply near the tank whilst the engine is running. You can turn the gas off with a valve on the under- slung tank, if you first put the van on ramps then crawl under it on your back. 

Without knowing anything about Paolo's fridge, I can't help him other than to say our fridge has an automatic selection button and we tend to switch that on and leave the fridge to find the best source of power.

If you have the Truma crash protection cut off, then you can travel with the gas on. We've been travelling with the gas on most of the time since 2000 when our van had an approved system. There are places where the gas/ignition should be off such as fuel stations and tunnels. Many motorhomers travel with the gas on and, it seems, at least as many insist on it being switched off.