Prices vary from region to region and studio to studio. Generally, franchised studios (Arthur Murray's, Fred Astaire, TC affiliates) sell lessons in "packages"...1 private, 1 group, 1 party...here in the midwest I believe that the going rate is something like $110 for this.Also, they usually work contractually. Personally I think it's pretty over priced...instead you might find an independent instructor...usually no contracts, little sales pressure...but charges by each lesson, or group lesson, or party. The going private rate i the midwest is $50-$70 per 55 min..
Most studios do not consider it their responsibility to find you a partner... you have to decide what yo are looking for first...competition or just social dancing? Then start looking around your city for dance related groups...goto studio parties, etc.. Finding a artner with whom you are happy can be a real endeavor. Good luck!