1000 a month for utilities whole house is high enough that it sounds like it could legitimately include the pool systems.

I don't really see why there would be a need for a cover. Indoor pools don't get wind so the evaporation protection isn't as necessary, and the safety aspect should be covered by door locks and door alarms.

You can look up local pool services to see what they charge, being indoors and saltwater biweekly or maybe even monthly might do (way less dirt getting in the pool, and saltwater systems need less frequent chemicals).

Most important thing would be to get a proper pool inspection done, by a pool inspector not just a home inspector or a pool maintenance company. Someone who will judge the state of the plaster, tile, coping, structure, and permanent plumbing of the pool. I can't imagine what significant renovations would cost on an indoor pool like that in new jersey but it could easily run into the 30-100k range so that would be the main major potential surprise.