I work in a fire district in the state of KY. I have two questions, please any help with the backing of KRS's and such would be great.

1. Is our department, being a public government have to pay holiday pay? I know private businesses in KY do not.....

2. We work a 24 hour on/ 48 hour off schedule, and we get vacation days to use each year with no carry over of them. Is is right/legal for our employer to tell us that only one person can use a vacation day at a time?

3. Lastly, does our employer have to give us paid sick time off or is that just a benefit??

1. Probably doesn't make any difference, private or public. If you were an employee of the state, maybe.
2. Not addressed by law so yes, legal. And makes sense. What would happen if there were an emergency and half the staff was on vacation?
3. Not by law, no.

Generally speaking, all of these issues are covered in a union contract. If you are a union member, you should confirm with your union steward whether your contract covers any of these issues. But without one, the law is silent.

on the vacation question, when more than one guy is off, due to injury and a vacation day or sick and vacation day at the same time, they bring in one person on over time to bring us back up to our lowest staffing number. So with that being said, there would be no problem with our responce number of personnel. So can they still only say one person off? Is there not a federal labor law stating that you can not deny time off unless you can prove a disruption in service??

Your employer gets to decide when you can take your vacation even with full staff unless you have a binding employment contract to the contrary.

No, there is no such federal law that you made reference to.