I am pretty sure you can LPG a diesel. There were are several companies doing it a while back but I don't know how successful or reliable it is.
Seemingly introducing LPG into the air charge makes the diesel burn faster and more completely giving more power which leads to better MPG.
I wouldn't use veg oil in the cdti - common rail doesn't like it very much (or so we are told) - you would possibly knacker your injectors and pump.
All diesel in the UK already has a % of bio diesel in it (max 7%) and this is warrantied by the Government to be ok in all UK vehicles. I think Renault have introduced some engines that they warranty to use up to 30% biodiesel.
Perhaps a remap may help increase MPG as long as you don't drive too hard. Also, keep your vehicle well serviced and make sure the tyre pressures are correct (maybe even put an extra couple of psi in them).
Don't use vegetable oil in a modern common rail engine. The injector pump will not get sufficient lubrication and will be (expensively) ruined.
Yes, I suspect diesel engines probably can be run (at least partly) on LPG. Closed waste landfill sites emit 'landfill gas', predominantly methane, from the decomposition of the waste. It's a requirement of the site permit that this should not be allowed to escape to atmosphere. The sites are capped with an impermeable membrane and the trapped gas is piped off. It is sometimes just flared, but if it is of sufficient quantity and quality, to prevent waste, it is used at a number of sites to fuel converted diesel engines which drive electricity generators. A small amount of diesel is still injected to stabilise combustion, depending on the quality of the landfill gas. Some 77MW of electricity are generated from landfill gas in the UK.
Whether a diesel vehicle LPG conversion is practical I don't know, but I suspect it would be costly>