1. DPF is a restriction in exhaust - restrictions in exhaust of any car will affect fuel economy
On top of that DPF needs to be regenerated which means squirting even more fuel into the engine during exhaust stroke to increase temperatures
so basically, remap == more fuel+more air == more exhaust flow == more backpressure
2. DPFs get blocked with two things soot and ash, soot is burned during regeneration and comes from not perfectly burned fuel, ash is coming from oil (that's why DPF cars need low ash oils) and fuel impurities, ash will stay in the DPF forever - it is the ash that causes DPF to fail after a while regardless of the driving style, soot does not cause any problems as long as you don't allow it to build up to the point where there is so much backpressure that engine can't increase temperatures to levels high enough to burn it off.
3. depends on the remap - good remap will not have any effect on trip computer readings, bad remap will make it show a lot better usage
This explains it very well, and it doesn't matter how much you pay for your remap - there are people that will charge you £700 for remap of that quality.
Because of the fact that bad remap like that will cause car to smoke more, the DPF will get cloged faster and need to be regenerated more often, also smoke == wasted fuel.