Perhaps there has been a miscommunication. It makes little sense for your group to employ these staffers on a temporary basis. They are school district employees. It’s not advisable or even practical for your parent group to go through the legalities of employing these workers, especially for one day.
A simpler approach, if your administrators allow it, is to have the district simply bill your PTO for services provided by school staff at the carnival. Your superintendent should be able to calculate the expense for each employee, including payroll taxes like FICA (the Social Security tax). Following the carnival, the superintendent would then submit a bill to your PTO, inclusive of all school employees’ wages and related fees. Basically, you would treat this no differently than hiring the services of a magician or musical entertainer for the school.
As for liability insurance, it’s a good idea for any parent group to carry insurance that covers both your group and your officers. Elly also strongly recommends bonding coverage for anyone who has access to your bank account.
If using school kitchen facilities and district nutrition services staff proves too costly or too complicated, consider outsourcing your carnival’s food operations to a local restaurant or caterer. Or, if space permits, rent portable grills or ovens and have volunteers cook the food on-site. (Check with your town’s public health and safety office and the fire department first to see whether this is allowed.)