You will need an OBD2 code reader. They can be found at most auto parts stores. It will tell you why it set off the engine light, and usually allow you to clear the fault codes.
i only want to repair my car without taking it in to the dealership, thank you
No there is not and the dealer definitely will not do it.
Yes.
looking at the engine right side by the rear head yo can see it without taking anything off
yes
Once you drive the vehicle away from the dealership you have taken possession of it and cannot stop payment for any reason without committing fraud.
No, because the engine just hangs off the back of the transaxle.
Yes is the simple answer. You may need gaskets if you do!
technically no! the only other way to do it is to still raise the engine off of the engine mounts at least a few inches.
There are a range of engine test equipment available in most very good Vehicle parts retailers
That's probably unburned fuel. The "check engine" light usually means you've got a problem with the engine emission controls. It's probably a faulty sensor or valve. I'd suggest taking it to a dealership to have the engine "scoped".
Drain out engine oil out, replace oil plug at the bottom of engine, pour in same amount of diesel let it stand 10mns, drain it and refill with engine oil.