Battery charging questions

[ahlem]

I have a 2001 3.0 M54.
The battery is about a year old.
The X5 is the third vehicle at the moment and sits as a backup until I can change the rear end bushings etc. (it started making unauthorized swerves in the snow)
I believe I hit the hatch button and it sat like that for some period of time. It sits outside because the e30's are hogging the garage.

Is there a sleep mode that would keep the battery from draining completely?

It's been in the single digits a few times in the last two weeks.
I went to move it today and the battery was pretty well drained to the point that a few dash lights came on but no crank. I jumped it using the underhood locations on both cars.

Can I put the charger on it using the underhood locations or should I unhook the battery and charge there?
What amps should I charge at? I have 2 and 10 and then a big jump assist of about 50 for a very brief interval.
I welcome your input. I drove around the block about 5x in second gear.