I recently bought a '06-Sportser from a guy and he had a four wheeler battery in it to ride it, but the bike was missing, back firing and cutting out real bad. Would having the wrong battery in the bike cause it too run like a car with a bad coil pack? Thanks for your answers in advance.

Sitting on the bike, the LEFT end is Cylinder number One and the RIGHT end is number Four. The Firing Order is 1,2,4,3. The coil packs fire repeatedly as left, right, left, right so you get that sequence.

go have a key cut using vin and use original pcm if you swapped out the ignition already then need to have all components programmed/flashed to the vehicle/ vin

The electrical problem of the other bike could've very easily fried your battery, too. It could have enough to turn over but that's it. Take your battery out, take it to a car parts store, have them load test it. It could just need a reconditioning and charged up.

Look on YouTube you may find more answers there

Check that the cam shaft is turning ( broken timing belt). run fault codes to determine if a position sensor has failed.

Bad sensor? Crank/cam. Coolant temp sensor?

The first thing that comes to mind is a bad head gasket and fits our symptom. Combustio

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Summary:
Monitor oil leaks: keep fluids topped up. Consider repair if the leaks are major.

Replace / Check: Idler tensioner - if this belt breaks you won't have cooling and the battery won't charge.

Miss-Fire: find the root cause and remedy poor fuel economy and can damage other components like the catalytic converter and these are not check to replace.

Don't spend $4200 with Mercedes - find a reliable mechanic who will do the work at a more reasonable cost.

I have to assume that the car looked & drove well when you bought it otherwise it would still be on the lot. I think $4200 seems a bit steep - The dealer you bought it off may be able to recommend a mechanic see them first but if not them certainly see another mechanic other than Mercedes - if you don't have a mechanic you trust head towards a larger franchise business in Australia we have places like UltraTune & K-Mart.

As far as what I would tackle - I am not sure what "Leaking Motor Mounts" - but I will assume there are some leaks - I would be guessing minor ones from the motor. Even though they may sound bad they are probably your lowest priority if they are small you do need to keep an eye on them however and make sure your fluids are kept topped up.

Get the idler belt checked - they can be a pain to try to do yourself get the belt replaced. Then look at your miss-fires. Have new spark plugs put in regardless (is my opinion). See if there error still persists if so then most times it is ignition coils that is the problem a mechanic can check this by swapping the 3 & 6 coil to other cylinders and see if the error moves, replace the affected coil. If the error stays on 3 & 6 it is likely blocked / faulty injector.
Carsales.com.au (This is AU pricing) indicates that you bought within a good price bracket.
2001 Mercedes-Benz C240Average Private Price+$10,000 - $12,300Trade In Price Guide+$7,300 - $9,600Average km+180,000 - 300,000Price When New (RRP)+$73,500

I can see if I can find more prices these are ALFA ROMEO prices (indicative). Ignition Coil: $150 - $250ea; Spark Plugs: $15ea; Injector: Service / clean remove / replace: $600; New Fuel injector: $300. Labour in AU charged by mechanics is around $95 - $180 per hour.

bad fuel or fuel filter is plugged start there

forget the ecm. ford computers virtually never go bad. sounds like an ignition module heating up and failing - a very common ford issue