By removing the ground wire from the battery and putting an amp meter in series between the battery and wire and measure the amp draw after sometimes 15 minutes.
The battery can be brought to many shops for a free test. Otherwise, you can test the voltage and parasitic drain amperage with proper usage of a multimeter, available at most hardware and electronics stores. To test the battery beyond voltage and parasitic drain, a very expensive piece of machinery is required to test it further. Most shops have such equipment.
A car battery in any car would drain due to a short in the electrical system.
If the ashtray light is not working it will not drain the battery.
You can get a car alarm that uses it's own battery so wont drain the car.
A starter does drain a battery. The battery holds a charge so that you can use your starter to start the car. After the car is started the alternator recharges your battery and runs your car and all it's accessories. If your car won't start or is having a hard time starting you can drain your battery by repeated unsuccessful attempts to start it.
If the alternator is installed incorrectly, yes, it can drain the battery.
Yes, if the relay was stuck it would drain the battery.
A stuck relay in the car can drain the battery. A dead cell in the battery itself will drain the battery overnight. If this is the case the battery must be replaced as there is no way to fix it. To find out disconnect the negative battery cable for around 8 hours. If the battery goes dead it has a dead cell. If not then something is draining the battery. Anyplace that sells batteries can test the battery for you.
leaving on the radio
No.
Yes
only if the car your using to charge the other on is not started