A vehicle may not run if the battery cables are disconnected with or without a bad alternator. The best way to test an alternator is by voltage output when applying a load.
The best way is to drive it to your nearest auto parts store and have it tested. You can test it somewhat yourself. Start the engine and use a volt meter to test the voltage that is being supplied by the alternator for the battery. If it is less than 13.5 volts the alternator is bad.
Using a Diesel fuel conditioner would be good for your engine and would not be bad at all.
run it and then disconnect the negative wire from the battery if alternator dies its bad.
Spark Plugs do not affect your alternator. As long as your engine is running then it should be charging unless your alternator is bad
The alternator must be running to test without disassembly. If you remove it, many auto part stores will test at no charge. One test is a voltage test. Start the engine and use a multimeter to check the voltage at the battery. It should read between 13.5 and 16 volts. Any less or more and the alternator is bad.
Check voltage with a voltmeter at the battery With engine running readings should be 13.8-14.2 With engine running hold a screw driver to the back of the alternator, if there is no magnetic field, the alternator is bad.
if your alternator is only 5 mon old you could have a bad connection on the alternator that isn't makeing good contact , or it could have a bad stator i would take the alternator back were you got it have them test it if its bad and it has a bad stator it might have warranty on it and they will replace it .
If it is makeing a noise or is not putting out at least 13.5 volts it is bad. Take the car or the alternator to an Auto Parts store and have them load test the alternator to be sure.
Yes, never put oil formulated for a diesel in a gasoline engine.
Yes, as long as you have a fully charged battery and good starter the engine will start even if the alternator is defective. The engine will run until the battery looses it's charge, which it will. if the alternator is bad.
Yes, because a bad coil will not allow the engine to run. But if the engine is running then the coil has nothing to do with the alternator charging the battery.