Yes. It is a myth that a battery will run down sitting on concrete.
Car batteries do not usually corrode just sitting on concrete unless their is a leak in the container. I do know that you shouldn't place a car battery on a concrete surface as it can cause the battery to discharge its self into the concrete and you end up with a dead battery.
No
No it will not, that is just a myth.
Jump the car from another car battery or hook a charger to the battery.
Leaving a battery sitting on a cement floor will have no effect whatsoever. It will not discharge the battery anymore than letting it sit in the car or on a wooden floor. That is a myth. Just put a charger on it and charge it. If it does not take a charge it is defective, but sitting on concrete did not cause it to go bad.
You can get a new battery, you can jump start the car with jumper cables and another car with a charged battery. You can also put a battery charger on your battery to give it a charge.
If the battery has more cranking amps than the recommended battery and will fit into the battery carrier box the answer is yes.
Is there power to the starter "S" terminal? What car?
No. This myth comes from two places. One, the cold of the concrete ruins the batteries storage ability. If that was true every battery would need replaced after every cold winter night. Two, the electricity leaks out of the battery because the concrete provides completed circuit. If that was true then why are batteries stored on metal shelves at part stores and car dealerships. Steel is a much better conductor than concrete.
Disconnect negative cable first from old battery and connect it last when installing new battery.
No
yes