I use a BB as well toading a Jeep....never had any of the problems you mention. The only time there is any real amount of electrical draw on the BB is when it is charging the air system...if the used system has a leak this could be the cause as it would be recharging often. as for the jeep plug hopefully it only blew the fuse (as it is designed to) as most standard cigarette plugs will not handle the continues amps needed to charge the BB system.
Call BB they will tell you the size wire needed to run the BB without overloading the jeeps wire, you may need to run a bigger wire. I have the wireless system that shows me when my BB is activated, this gave me the ability to better set the sensitivity of when the BB activated, there by not putting on the jeeps brakes unless really needed and limiting the recharge of the system.
