Something else can be on. A interior, trunk, under-hood, glove box light. Also a relay may be stuck. It can also be the battery has a dead cell which will drain it overnight.
Yes. Otherwise you will drain the battery through the ignition points, burning them out prematurely or even welding them together.
There's something left in the car that use power even when the engine is off. Can be a dashboard clock, can be the vehicle alarm system, can be the stereo. The battery can also have a dead cell which will drain it overnight.
Almost anything. On newer model vehicles, the engine's computer drains the battery constantly, as does the stereo. Short circuits can cause a drain. Any electrical system that is left on will drain the battery. Even a disconnected battery will lose charge over time and the older the battery, the faster it drains. Also a battery with a dead cell will discharge itself, usually overnight.
In a modern car there are a few things that are still "on" even when the ignition is off, there's a clock in there somewhere, you've probably got an alarm as well ASO. It isn't much, but enough to drain a battery if left long enough, particularly if the battery isn't 100% to begin with.
Something is causing a drain on the battery even with the vehicle off and nothing turned on. A good mechanic can do a drain test on the battery to see what may be draining the charge. A dead cell in the battery itself will also cause the battery to go dead. Disconnect the negative battery cable overnight and if the battery is dead the next morning it has a dead cell and must be replaced. If not look for a light that is on or a relay that is stuck.
Computer modules are supposed to "go to sleep" about 15 mins after you shut off the vehicle. If they don't, they can drain the battery. See related links on how to find the bad module. The battery itself may have a dead cell which will cause it to drain overnight. If that is the case the only fix is to replace the battery even if it is a new battery. It may also be you have light that is on pulling power from the battery. Under hood, trunk, glove box, dome light, brake light, etc. You could also have a relay that is sticking.
If you have checked the battery and made sure that the new alternator is working, the only other possibility is that something is staying on when the ignition is off. Not all new alternators are perfect, sometimes they come with a faulty component that can drain the battery. Also, older batteries can slowly drain if the plates are starting to fail. It's difficult to just give one solution to a problem with so many possibilities.
A battery that runs down overnight is normally caused by a dead cell in that battery. The only fix is to replace the battery. It can also be caused by any light that is left on, on the vehicle. Dome light, under hood light, trunk light, glovebox light, or even brake lights that our on due to a sticking brake light switch. A relay that is sticking can also cause this. Disconnect the negative battery cable and let the vehicle sit overnight. If the battery is still charged the next morning then you know the battery is good. If the battery is dead then you know the battery has a dead cell and must be replaced.
battery, solenoid/starter or relay or even ignition switch
Most often it is the starter and not the ignition.
I've just installed a new car radio, and even though it is switched off (and the face has been removed) with the rest of the car completely off, the battery is flat 2 days later. You have a dead cell in the battery or something else is on draining the battery. A radio that is not on will not drain a battery in 2 days or even 2 weeks.
Yes, very, very, quickly. The Starter Motor has a very high operating current, that will drain even the heaviest duty battery, fairly quickly, if an engine fails to start.