Some of it I've heard before, and some of it I guessed based on what I assumed the writer's attitude was.
For example, on the first question, about the handshake: Personally, I lean more towards interpreting a "double handshake" as glad-handing, dominating, politicking, image-sculpting, and manipulative. Normally. On the other hand, if the person doing it is, for example, a small, soft-spoken woman who collects rabbits as a hobby (I'm using this as an example because I know this person), I'm more likely to interpret it as being one way that she tries to "connect" with people. I might feel a little smothered, and I might be concerned that I'll offend her somehow and run into some kind of quiet damnation from her, but I probably won't feel like that particular person is being a politician and trying to dominate while seeming likable, like I would in the first example I gave. It depends on how I read the other person's intentions and general character. It's based on experience. I don't know people who clasp my hand that way because of "trust", inasmuch as I've ever read it to be, but I knew that was the answer the quiz writer was going for. How did I know? Well, I really just assumed, and I assumed correctly.

I thought that in the writer's eyes, the "dominance" answer would seem too "negative" or like too much of an assumption. I imagined that the writer would interpret the "dominance" answer as being a little paranoid or not being able to read intentions.
That's a little bit of a circular explanation, since it keeps coming back around to what I assumed, and to what I thought the writer would assume about me, etc. Maybe it clarifies my reason to some extent, though.
Some I'd already heard before, like the smiling & eye crinkles one and the "attempts to cover their mouth" one. I disagree with both of those, to some extent, though.
1) Smiling: A smile isn't fake just because you did it on purpose. It might not look as nice as a whole-face smile, but I frequently smile deliberately, yet stiffly, in an effort to convey my sincere good intentions. I'm not naturally smiley. I really love it when people take my effort at face value and seem to recognize that I'm smiling in order to convey friendliness or good will.
2) Covering your mouth and other parts of your face can mean that you feel shy, or that you're politely holding your tongue because you don't want to interrupt, or that you're bored or tired. You could make a case that some of those constitute "not telling the whole truth", but the implication is that this action conveys untrustworthiness, and in a real situation, there's more context, and it might (A) mean something else and/or (B) be read differently. It also might be read differently by different people, based on whether they can relate to that context or not, and how they relate. It also can be read differently by a single person, depending on mood and outlook at that time.
Also, with the "might not be telling the whole truth" question, one of the options was "they make steady eye contact". I've actually heard that this is sometimes considered an indicator of lying. I didn't think it was the answer the quiz writer was looking for, though, because the face-touching one is standard advice. I've heard both, but I went with the one that was more likely to be on the author's mind.