Black smoke from the exhuast when acelerating

question edited for clarity and toss in some CAPS.
Question moved to model category.

Camshaft Position Sensor Location

Range Rovers Forum https://www.rangerovers.net > threads > camshaft-posit...
Nov 5, 2021 - It's right under the VVT solenoid on the upper timing cover. 2 per cylinder head, 4 per car. Part LR014372, however a Bremi 31491073 is the same ...

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Question edited for clarity.
Question moved to model category.

some ideas here

https://www.google.com/search?q=2010+Range+Rover+Sport+%22suspension+fault%22+the+car+raises+to+off+road+height+while+driving

..

https://www.rangerovers.net/forum/6-range-rover-mark-iii-l322/239242-2009-hse-range-rover-transmission-fault-p0730.html
https://www.rangerovers.net/forum/9-range-rover-sport-l320/267530-transmission-service-p0735.html
https://www.rangerovers.net/forum/9-range-rover-sport-l320/48932-range-rover-sport-2012-transmission-issue.html
https://www.yourmechanic.com/article/p0746-obd-ii-trouble-code-pressure-control-solenoid-performance-or-stuck-off-by-valerie-johnston

i'd suggest getting the cylinder compressions checked , black smoke indicates burning oil so could be piston rings , also that would explain lack of throttle response and low revs

The brake light fuse lives in the boot on a Range Rover Sport - lift the access panel and its on the Left side in a bank of 4-5 fuses immediately neighbouring the jack slot.

Sometimes it does and sometimes it doesn't.

>> somebody that work in the dealer told me that they just have to program it unlock it

Go back to that same person, and ask them for the details.
If she/he cannot provide the details, it's likely that she/he was just "blowing-smoke".

how do you change km to miles on a range rover sport se 2005 model

range rover sports 2005-2009 cigarette lighter is number 55 on fuse box and is a 15amp,the car takes bussman fuses(ie) small fuses

This is just a WAG, but I would say you didn't replace the fuel filter after you replaced the fuel pump. Sometimes a stronger fuel pump also pump more of the accumulated gunk from your tank into the fuel system, so the filter clogs up faster.