Floor tile replacement
 

Could someone recommend a handyman that replaces broken floor tiles in my villa?

First question, do you have replacement tiles? If not, call home warranty, and ask for the original supplier and the tile name, etc. call the original supplier to see if you can get replacement tile. If you can, send me a PM, my step son does really nice tile work, 2 decades experience.

Cover them with vinyl plank

Be careful if you just cover a tile floor, especially the kitchen with another flooring product. this raises the level of the floor 1/4 inch to 1/2 inch and you may not be able to remove and replace the dishwasher, or any other built in appliance due to the lower clearance, had this happen back up north, and had to jack up the counter top to get the dishwasher out. Fortunately it was laminate and not glued well!