The "Turing Test" is generally taken to mean an updated version of the Imitation Game Alan Turing proposed in his 1951 paper of the same name. An early version had a human (male or female) and a computer, and a judge had to decide which is which, and what gender they were if human. If they were correct less than 50% then the computer was considered "intelligent."
The current generally accepted version requires only one contestant, and a judge to decide whether it is human or machine. So yes, sometimes this will be a placebo, effectively, if we consider a human to be a placebo.
Your first and fourth questions are related - and there are no strict guidelines. If the computer can fool a greater number of judges then it will of course be considered a better AI.
The University of Toronto has a validity section in this paper on Turing, which includes a link to Jason Hutchens' commentary on why the Turing test may not be relevant (humans may also fail it) and the Loebner Prize, a formal instantiation of a Turing Test .