House empty: no one in it.
House vacant: people have left the house so that it is empty. More or less synonymous with empty.
You cannot say: the house is free. You can say : 'the bathroom is free', because it refers to a short-term use or non use.
Is this seat free?: Refers to short term use. It means: is someone using it, or can I use it>
Is this seat vacant is almost perfectly substitutable for 'free' in this sense, but it is slightly more formal, and has a different emotive connotation.