Jeremy Dover left a great comment that inspired this answer. I am only interpreting the question differently than he did, which very slightly changes the answer. He indicated that there is no minimum.
For history's sake, at the present moment the puzzle states: What is the optimal strategy (fewest questions) to guarantee that you know which one is Alice ...
Truthfulness: T(ruth), L(ies), F(aithful)
Let's start with Mirror 3. It
With only 2 truthfulness options left, Mirror 1
And with that, Mirror 2
Summary of findings so far:
With our good friend the checksum (thanks for that, OP!), here's what we get.
So this is where I'm scratching my head. If I go by the connections being the letters to look at, I get
THIS QUESTION HAS BEEN CHANGED IN ORDER TO MAKE MY ANSWER INCORRECT!
Previously the question said "Bob is a random (randomly tells the truth or lies)". 15 hours after my answer (and after a discussion in the comments) the question was changed to say "Bob is a random (he randomly answers yes or answers no)". This can be ...
Please read first: The question has had a recent edit which, although looks similar, is a subtle change which makes a big difference. I believe my answer below is the correct answer to the question in its current form.
However, the question previously stated that Bob randomly tells the truth or lies, that is to say, Bob cannot make a series of ...