Leave it connected. If it is a good battery you will be okay. If you absolutely need to disconnect it, then disconnect the negative cable attachment at the battery. You will need a good quality 5/16 wrench.
You have set the alarm off. You will need to turn the alarm off before you can do anything else. If you don't have the alarm fob, then have it towed to the dealer so they can go through the special procedure that will turn it off.
ABS is wonderful when all conditions are correct, but troublesome as dog doo-doo when not. When it's slippery out the ABS cannot know that, and tries to make your tires work correctly anyway, often times completely screwing things up. You are doing what you can, just keep pulling over and...
It could be the wiring in the steering column, but definately not the plug wires...if that's what you meant by "wires". More likely the ignition switch is the culprit.
You can put any battery that will fit into the car in it, so roll on down to a battery shop and do it; get their best battery, and make sure that it will be held in place by the hold-down block and not jimmy-rigged. Often times a battery line has a "universal fit" battery, and they work well so...