Well, as best I can tell, the specs say gas electric refer. Have you looked at the manual for the refer? You can run it on gas, as long as you don't go through a tunnel. Might also want to turn it off while refueling. A few other suggestions/questions about running a refer on gas while towing have already been discussed on here. Do a search and ye shall find.
Also, as for water on the counter tops, there should be a small drain hose, just below the freezer, that runs to the outside lower vent, at least there is on most refer's. Not sure how you are getting water on the counter tops, as the door gasket should keep all the water in the refer, even if that line was disconnected. Something to check.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT