So what is critical thinking in your mind?
IMO the item labeled 1. contains two distinct questions – each with it’s own question mark. So too, item 2. could also be divided into two questions. It that observation a quible or a sign of critical thinking?
I theorize that the ‘mismash’ of responses the OP received is influenced by the imprecision and looseness of critical thinking of the questions posed .
Also the more tightly the OP is written the fewer responses one gets. Assuming we prefer our OPs receive more attention in the form of responses there may be a powerful motivation to avoid using too much critical thinking in the composition of the OP!
critical thinking with respect … to examining contemplative claims & practices?
In what sense do you mean by “examining contemplative claims”?
To what extent is critical thinking an essential component of contemplative practice?
A prior question might be “to what extent is critical thinking a desirable component of writing posts on suttacentral?”
Maybe the smart thing to do is leave some of the thinking to the reader.
On the other hand in the EBT’s the point of a story or analogy is often explicitly pointed to. 
The Buddha didn’t mind “explaining the joke”.
The form of the EBT’s reflect a lot of critical thinking. So to the extent that contemplative practice involves reading , understanding and reflecting on EBT’s then some degree of critical thinking is required.
As I see it there are many forms of critical thinking. People frequently employ forms of critical thinking without thinking about it. To the point that many might deny (at least at first) that they are using critical thinking – rather it was ‘common sense’, ‘from the heart’, metta, moral reflection, etc.
A huge challenge with critical thinking is knowing when we are using it or not using it.
So it’s also important to have supports and scaffolding in place – ‘spiritual friends’., (Iti 10 - see @Mat 's posts in this thread)
What I hear from accademics and teachers is that teaching critical thinking is challenging and measurable results of such training is weak to lacking.
Often critical thinking and/or science don’t lead to a single or clear conclusion.
- I identify with the school of the philosophy of science that says that all science requires a degree of subjective, expert opinion/judgement.
Re: “System 1” and “System 2” thinking. They interpenetrate each other in several ways.
All “system 2” thinking is first “system 1” thinking – all thought is first pre-conscious, we can only rationally think what our sub- or pre-conscious mind allows us to think.
Then, related to the necessity of judgement …
Over the course of the last decade, Cultural Cognition Project (CCP) researchers have focused on the relation between conscious, effortful “System 2” reasoning and public controversy over science.
Many commentators attribute public controversy over science to overreliance on “System 1” reasoning, which consists of experiential and heuristic assessments of information. Contrary to this surmise, we have consistently found that one or another critical reasoning proficiency—from science comprehension to numeracy to cognitive reflection to actively openminded thinking—magnifies rather than dissipates partisan polarization on issues such as climate change …
The better we are at critical thinking, the more informed we are … the better we are at justifying our position. Be it on interpretation of the EBT’s, science, compassionate action, or social justice.
[ 
Added: One could argue, with good reason, that so-called ‘critical thinking’ used as a way to ‘rationalize’ our positions (the positions we are attached to) might be better described as somewhat _un_critical thinking.!]
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References:
See fig. 1 from this paper from this short Cultural Cognition paper.