It would be an oxymoron, as homes stand, not lay on the ground.I would personally go with "My homes are vacant.", or "My homes are standing vacant."
The public is correct. plural and singular verbs can be tricky... but you use a singular verb with a singular noun, and a plural verb with a plural noun. For example: The person (singular) is...
You could say " It's him ! The man I saw following us." Or you could say " It's he who wants to go not I."
The phrase would be written, "That's yours".
Corr.