The ground and first floor of the property were damaged by the fire
Note: it might help you if you consider the word floor to be elided or left out of the sentence after ground. Saying floor twice is not necessary.
You can rewrite the sentence as
The ground floor and first floor of the property were damaged by the fire
Floor in both sentences is a singular count noun. Hopefully you know that count nouns can be either singular or plural. This is one reason they are called count nouns. You can count them. As in
How many floors (levels/stories) does that house have?
It has two floors (levels/stories), the ground (floor) and first floor.
I have two hands, my left (hand) and my right hand.
I can elide or omit the first use of hand here. Saying it twice is not necessary.
In another article, the count noun floor is used in the plural:
Firefighters were called to the Llandeilo blaze at about 03:00 GMT on Thursday, with the ground and first floors of the property damaged.
So the answer to your last question is that you can say either "the ground and first floors" or "the ground and first floor". And you can say either" the ground and fifteenth floors" or "the ground and fifteenth floor".
In England, you walk into the ground floor and walk up one floor to get to the first floor. In the US, you walk into the first floor. (Exceptions can include when a building is built on a hill and on the higher side of the hill you walk into a floor higher than normal.)