The battery

Can a person jump a totally dead battery that has been drained over night because the door was a jar? Or should a person charge the dead battery with a battery charger first? What are the risk to a perfectly brand knew battery if any?

It’s best to charge with a battery charger first. Risk to a brand new battery that was discharged? Probably a shortened life.

I think the greatest risk of a possible issue is if you try using the alternator of the car to charge up the drained battery. That puts a big strain on the alternator and may damage the diodes inside it. You should use a battery charger to get the battery charge back up to full charge before using the battery again. It will take a number of hours, even using a 10 amp battery charger, to get back to a full charge on the battery. The lower the recharge rate the better it is for the battery. A 2 amp rate is real good but that will take perhaps more than a full day to recharge the battery.

A lot depends on the quality of your jumper cables. When you attach them, the drained battery will draw current and when you crank the starter, it will add to the the current draw. You likely will not start the car. If you have no options except jumping, connect the cables and let the dead battery charge a bit before trying a start. It is safer to charge the battery at a low level all night before attempting a start.

If you are putting a small charge on the dead battery from the alternator of a donor car, do not rev the engine on the donor more than 2k. This will limit the output current from the alternator to a safe level. Above that, you can overheat and burn out the diodes. Just letting it idle would be the better, but not as good as removing the dead battery and having it charged on a battery charger.

Many jumps are to totally drained batteries due to light being left on etc. In this world of minimalism and computer controlled cars I am much more leery of jumping a vehicle than I used to be. My wifes car had a sticking brake light switch, I have a battery maintainer for the boat, and it would charge the battery to start capacity in about 20 minutes. Using an alternate source to charge the battery is what I would recommend these days.