The NSX is very stiff and the hanging weight of the car will not hurt. We recommend car stands on the rocker between the tires. Also, putting the car on jackstands allows you to periodically spin the tires by hand, so as to keep the wheel bearings and CV joints happy. There is a good battery charger available from 1800 Bass Pro, will turn its self off at 14 volts. The car locked with the radio memory and alarm does draw from the battery - about 4 to 5 milliamps.
Moth balls seem to work for some people under hood and around the engine.
Rodents like coolant hoses, wire insulation, brake lines, etc. Battery See the Maintenance - Battery section for information on keeping the battery charged. Use about 5lbs. for interior, 3lbs. for the trunk. Do NOT put this stuff directly on the leather or dash, you will get marks. Put it on a towel.