Re: "a vacant table", "a free table", "an available table"
:up: All correct, but not always interchangeable. 'Available' rarely (if ever...:-?*) precedes the noun it modifies, but a table can be either 'free' or 'vacant' or 'available'. And, referring to a chair (say, in a pub where you were trying to seat 5 people around a table with only 4) you'd say (to a neighbouring table with a vacant chair) 'Is this free?', rather than 'vacant' - which it obviously is. In that situation you could also invert the question to 'Is this free', or leave the verb up to the audience's imagination and say (with an appropriate mime) 'Do you mind if I... ?' (by which time they'll have said 'No, it's all yours/go ahead/be my guest...' or 'I'm afraid it's taken').
PS* No, of course not - in, for example, 'they sat at any available table'.