Rough Idle and at 4000 get a misfire - 2004 Mercury Montery

rough idle symptom of misfire --need to diagnose if plug wires/coil failing injector etc ---noise can be anything from debris to failing suspension part need to jack up and inspect

need to find out why the misfire bad coil ,wire ,wrong plug gap etc check injectors and fuel presure --what ever is causing misfire is also probably causing problems with transmission shifting

rough idle is from faulty injectors or maf/vaf sensors or vacuum leaks
run the fault codes to determine the fault area

hot or cold. or both
what is RPM at rough idle, too low,, below 800 rpm?
its misfire, do a tune up.

Brake switch out of self test range,
Rough idle can be from uneven cylinder compression to worn,to the ignition coil sorting internally, the strategy of the PCM does not have to code up a misfire until it exceeds a misfire value, With a rough idle you need to check the basic

did it misfire before the tune up? if not more than likely the firing order is wrong the wires we're put back onto the plugs incorrectly check the order other things that can cause this are fuel or even a vac. leak

try your coil packs they go over your sparks or do plugs first and see what happens do affordable first

The Misfire is your Rough Idle check Coil Pecks & Spark Plug Wires

all the codes you have are all related to the fuel trim, this problem needs to be looked at with a european capable scanner for futher tests sorry.

you haven't said if its petrol or diesel so i'm assuming its petrol since your smelling sulfur sounds if you have a misfire causes could be plugs,leads or ign coil i suspect its ign coil these are common to go.