fix what battery arc from installing battery cables backwards?

Car: 1995 BMW 740i mfg 10/95
New Battery installed backwards that caused an arc.
The car alarm sounded and wouldn't disarm with the key in the door or ignition. The alarm fuse had to be removed for it to stop. My remote key doesn't operate (door locks, and alarm of course.) The interior lights on ceiling do not work, nor does my back up lights along with my windsheild wipers. I guess I'm lucky it starts and runs. The message on the dash includes: Trans. failsafe prog. where the car is operating only in 3rd gear. I took it to a certified shop that stated he wasn't able to access codes from my general module, therefore it either lost it's memory, or needs replaced, and unfortunately the programming is a "dealer item" only. If replacement is required, a used one would be sufficient and gave a referral to acquire one if needed. The module is obtainable used for about $250 and they referred me to an electronics person that could program it to my car. I have not yet purchased a module, but I took my car to the refferal as he said he could analysis my car and telll what was wrong. 3 weeks later and still not fixed, he acquired access to 3 different modules that he installed that didn't make any difference, then said he found out that the module needed to be from a car of the same mfg date as they changed the programming regularly so they wouldn't be interchangeable.
Can you tell me what your opinion is of the problem to address for all that was effected from the battery arc? And do you know the specifics regarding the general module for replacement? And what could be the outcome once the module is replaced? Could it then be the opening of whatever else may be wrong? I really have enjoyed this car and would like to keep it without becoming buried or upside down in fixing this situation.