i dont know about remaps and am failry sure they still arent possible at these, i worked at one of the largest remapping companies until about 6 weeks ago.
in terms of the "boxes" you refer to, they plug into the fuel rail and send a false signal back to the ecu saying it is at lower fuel pressure than it is. in turn the ecu corrects this by increasing fuel pressure.
the science behind this is squirting fuel at higher pressure not only puts more in to give more power, but also gives a finer mist of fuel which is meant to give a cleaner burn and more efficiently use the energy in the fuel.
yes they can give more power and yes they can give more economy.
now the downsides, firstly high fuel pressures mean noisier injectors, this isnt a problem for everyone but some people dont like it. secondly it will increase injector wear, not significantly but on an old tired engine its something to consider.
and finally on the economy front, DO NOT BELIEVE THE GAUGE, the box has sent an signal to the ecu saying it is at lower fuel pressure than it is. this causes the ecus fuel calculation to think it is injectining less fuel than it is, the increased reading will therefore be more than the actual gain. brim to brim is the only way to compare.
unfortunately the increase in consumption is probably not significant to not put down to environmental changes. what electrical systems are on in the car, ambient temperature, temperature of the fuel when it was underground at the pump, hills, driving with a head or tail wind, number of people in car blah blah blah.
sorry for the essay just thought id share my knowledge on the tuning boxes to help people with the decision on if they are worth it.