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.
As long as the cables are connected properly.
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.
no as long as you don't put the cables on wrong
not possible
Replacing a car battery normally takes about 5 minutes unless there is a problem such as corroded wires.
It is important to replace the battery with one of the same amperage. The number of plates do not matter. If you replace your battery with one of lower amperage, it will not last nearly as long.
A long slow trickle charge (3 amp or less) is always best for the battery.
Does the engine turn? It might be a problem with your battery If your battery is faulty it will not retain charge for long, try using another battery or use a jumper cable and another car/battery. If it starts then replace your battery. If the engine turns but does not start then the engine needs tuning.
How long was remote left without battery. Information stored may be lost if the new battery is not in place fairly quickly. You may need to have your remote recoded.
battery is low charge. Take it for a long drive, to take the load off the engine from the alternator charging it.
The battery will discharge if left for a long time as some current always drains to Earth. They can normally be recharged.
As long as the battery is correct specification, and serviceable it will not affect the car. The problems start to accrue if the battery is not large enough or getting weak. If the battery voltage drop below 11 volts the vehicle will start to give fault codes.