Corroded or loose battery connections, loose alternator drive belt, defective alternator, or dead cell in the battery.
If the battery was charged when you installed it, you do not have to drive the car at all. If not you should charge the battery and not use the cars alternator to charge it.
I assume you mean how long to charge the battery. You should never let the alternator charge a dead battery if possible. The alternator is designed to keep the battery charged but not to charge a dead battery. You put a strain on the alternator and it can cause a diode to burn out. Drive home and then put a battery charger on the battery to fully charge it.
You should never drive a car around for long after jump starting a dead battery. This puts an enormous strain on the alternator. Alternators are designed to keep a good battery charged, not to charge a dead battery. You can easily burn out a diode in the alternator. Jump start the engine and drive it somewhere and connect a battery charger to the battery and charge it fully.
battery is low charge. Take it for a long drive, to take the load off the engine from the alternator charging it.
It is best to drive home and put a battery charger on the battery and let it fully charge. Letting it charge with the alternator puts a strain on the alternator and should be avoided if possible. But if you have no charger then you will need to let the engine run for around 30 minutes to charge the battery enough so that it will start the next morning. It will take a couple of hours of driving to fully charge the battery.
The alternator charges the battery whilst the engine is running via a drive belt that runs off the crankshaft pully
One of two things is normally wrong. Either the battery has a dead cell and will not accept a charge, or the alternator is defective. With the engine running at idle check the voltage at the battery with a digital voltmeter set to the 20 Volt DC scale. If the alternator is good you should read from 13.5 to 15.5 Volts. If the alternator has a separate drive belt then it is possible the drive belt is broken.
I drove mine today, it was fine while the battery had over 9 or 10 volts, but once the battery died, the car (4WD, mitsu challenger) started driving poorly, and then stopped when I pulled over. Not sure if I did any damage yet. If it is a SI (Spark ignition) engine then you can drive so long as the battery has sufficient charge. A CI (Compression ignition) engine does not rely on an electrical ignition and will drive without the alternator or battery.
The battery only stores electricity, it does not create it. The alternator puts back the energy that was used by the starter and also provides enough electrical energy to keep the accessories running without draining the battery. If the alternator isn't operating properly the battery will discharge. Many auto parts retailers will test your alternator for free in hopes of selling you a new alternator or other part that will help you solve your problem.
Yes, the battery starts the engine, and as long as the battery is fully charged the engine will start. The battery will loose it's charge if the alternator is defective and not replenishing the charge of the battery but the alternator has nothing to do with starting the engine.
Yes, once you have jump started the car (from another car's battery), driving the car will recharge the dead battery (provided the battery is OK). This is a terrible idea and may damage the alternator. Drive the car immediately home and charge the battery with a battery charger. Alternators are designed to keep a charged battery fully charged. They are not designed to charge a dead battery. This puts way too much strain on the alternator circuits.