How do I change the number plate lamp on a merc A170

https://www.youtube.com/watch?v=q1M9La-uOt4

Thats news to me. I doubt any manufacturer would miss out the chance to charge out for a replacement fuel pump.
However, A class cars are a real pain to work on and nothing is easy. I suggest you lift the rear seats to see if there is an inspection plate, if so remove plate and you should see the top of the fuel pump/ fuel sender unit. Unscrew cap and carefully lift assy out. Remove pump and fit new part. On reassembly be sure to really tighten screw cap back in correct position or it will leak fuel.
Good Luck :

For you to check the gearbox oil there are three different types of dipstick depending on the model of gearbox in them,and the gear oil has to be at running temperature to be checked.

You must have the engine computer scanned for fault codes, very seldom does a fault disable the engine.

try removing the radio and getting the numbers off the back and call merceds. on ocasion it might have to be sent to the factory to be reset

you need a special reset tool.

A quick phonecall to the service department of your local dealer should confirm what they should be. Alternativlely you could check the current tightness of the bolts on the caliper you haven't disturbed yet. I'd estimate around 60nm should be correct.

There is usually a fuse box in the spare wheel compartment, there is also one under the rear ,Owner's manual indicates fuse position

i found the solution to same problem here.
http://mbworld.org/forums/e-class-w211/314638-no-power-trunk-3rd-brake-light-license-plate-lamps-2.html
it was a easy fix, broken wires in the boot a common fault with mercedes.

hi,pls.check the fuse in lighting switch, check contact on terminal 12 and 13 of lighting switch,or how about the bulb,continuity between switch and plate light connection,if all is ok,your switch not supplying power(defect)ty