1) Cling film. Cost: zero (to the nearest penny). Availability: In your kitchen. Don't forget to ask permission first!
2) The fridge uses so little gas that covering up the vents will not make any difference to it working or not. The fridge does not take any significant air from the vents, it usually takes its combustion air from the habitation area ventilation. It does not emit carbon monoxide from burnt gases into the habitation area.
3) Personally I can't work out why these vent covers are supposed to make the fridge work better. I thought that Newtons law of cooling said that heat lost from inside of fridge = heat gained by outside air. Or another way of putting it is that the greater the temperature difference between two surfaces or bodies, the greater the heat transference. In other words if the fridge coils are at 60 degrees and the outside air is at 40 degrees, there will be less heat transfer and therefore less cooling inside the fridge than if the fridge coils are at 60 degrees and the outside air is at zero degrees.
en.wikipedia.org
4) the reason your jets get blocked every year with muck and rust isn't exactly to do with the fridge being old. The rust comes from the steel 'chimney' immediately above the flame which emits water vapour as well as the burnt gases. If you dismantle the chimney and burner and scrub out the inside with a wire bottle brush it should last several years before needing doing again.
If the chimney is that badly corroded that it needs cleaning out every year, get a new chimney and flue assembly.