Timing chains on r53 don't need changed unless they stretch or start to rattle, fuel pumps very reliable as well, I think your confusing r53 with r56.
There is no fault with any sensors or fuel pump.
would of helped if in your first post on this subject you added what mini as most do, the r53 has electronic constant pressure pump in the fuel tank 4.6bar on post 2004 and 4.2 bar on later ones, no fuel regulator valve as such just regulated by the fuel pump output, fuel is then pumped in to the fuel rail at this pressure where the injectors turn it to a gas ie atomise the fuel, where the later turbo cars do have a fuel pressure reg.
as for r53 dont ever have timing chain problems good luck with that belief after 100k they tend to get pretty worn by 150k, they dont tend to snap they just rattle when totally worn out, another thing i have seen a lot on 100k plus cars is camshaft wear is fairly high on driven hard cars, just done one on 2002 100k on it camshaft lobes had over 5mm missing off the lift this car would not rev right,, it also had all valve steam seals gone large build up of oil burn crud on backs of exhaust valves ie restricting the gas flow some what also added to a flat running car, the car came in pressurising the coolant system and had a fair bit of oil in the coolant,, so its had gasket done and new water pump and serviced the charger and high lift cam shaft set of cooler plugs and new oil cooler... and all the inlet black coated and super charger etc to deal with the heat better,, it also had a new timing chain kit to ensure it was all in time,, to be clear all these single link chains all wear most car makers now put a 100k to 150k life span on them, but on a lot of cars like the prince engines and some of the vag cars barely do 60k , 20 years ago all car engines with timing chain were indeed life of engine and could do 200k 300k even on some as were duplex chains and good metals used.
on this mini just done i set the crank at tdc and set cam to where the new chain is correct then i put old chain on sprockets without moving the crank or the cam and the them put two marks and then moved the crank until the old stretched chain was tight again and measure the travel, ended up with 3 degrees retarded,, trouble is with a super charged engine with a smaller sprocket and then add retarded timing will add to the already out of fuelling the small pulley gives ie more air to same amount of fuel hence why they need mapping to match the fuelling to get then 14;1 ratio and engine likes to be on
also flat running cars r53 the bypass valve can fail or stick, also if super charger makes any metallic noises its going to need stripping find out why as could be bleeding off boost, measure the out put of fuel at fuel rail
