I've managed to buy the worst car in the world ever.
Hi Andrew - please fill in your profile with UserCP ^^^
I bought a similar CLK 240, 2004 model in 2006, and it's been as good as gold. It's never been inside a workshop to date. Does your have a huge mileage?
Some of your problems are known here.
a) coolant leak into gearbox. Yes, the well-known Valeo radiator problem, solved in 2003.
b) sear belt broke. How ???
c) locking wheel nuts jammed... Not an MB issue.
d) cluster refurbished. Surprising.
e) stuttering. What was that? MAF?
Ref your spurious alarm situation. It could be caused by many things. Coupe or cabrio? They have different sensors, etc.
If you lock the car using your remote, and then unlock the driver's door using the 'mechanical' key, you will not operate the central locking system. When you open the door, the alarm system should be triggered. Inserting the key into the ignition switch should reset the alarm system. Try that and report what happens.
Forget the siren not sounding. Often they have been disconnected by a previous owner, or have died of old age.