As I see it, the paper is not trying to do any of that. The introduction is explicit: instead of trying to definitely answer the question "Can machines think?", it suggests an alternative question we can ask that can be specified much more precisely. "Can machines think?" is vague and open to many possible interpretations; in contrast, the paper proposes a question that is less ambiguous.
(Implicitly, the implication is presumably that this shift of perspective might be interesting and help us think more clearly about the topic. But it's up to each reader to form their own opinion about whether they find this interesting or useful in clarifying their thinking.)
This purpose is explained in clear and direct terms in the essay, particularly in the first paragraph of the essay as well as the second section of the paper.
To answer your specific questions, here is how I read the paper:
No, the paper is not trying to definitively answer the question of whether it is possible for a machine to pass the Turing test. Rather, the paper is suggesting that the question "Can a machine pass the Turing test?" is an interesting question, worthy of our attention.
Think of this like a scientific paper that proposes an experiment -- it's not necessarily trying to persuade anyone about what the result of the experiment will be, but rather suggesting that the experiment would be an interesting one to carry out or to consider. That can be a useful, even ground-breaking, contribution.
No, the paper is not arguing that passing the Turing test necessarily signifies intelligence or thinking. As far as I can tell, it doesn't take an explicit position on that.
We could imagine that one position that is compatible with the essay would be to say "I'm not confident I could define exactly what counts as intelligence or thinking -- that seems hard to define -- but whatever the answer is, passing the Turing test seems like it would be a significant milestone." We could also imagine that another position that seems compatible with the essay would be "Yes, according to the way I personally define intelligence and thinking, passing the Turing test would signify intelligence and thinking."
No, I think it's pretty clear that Turing is not claiming that the metric is purely arbitrary. On the contrary, the essay tries to argue that investigating this metric is worthy of our time. See, e.g., section 2, which begins with "The new problem has the advantage of...." You might find this argument persuasive, or you might not -- you might find the paper's proposal worthy of our time, or you might not -- you might find the paper's proposal arbitrary -- but I don't think it's fair to say that Turing thought the question was arbitrary.
These are my personal opinions and interpretations of the paper. Others might vary.
Note that I've answered the question "What is the essay arguing?" I haven't tried to tackle the question "What did Turing think?" since it can be hard to know what someone is thinking, and it's easier to grapple with the intellectual ideas as expressed in a particular paper.
Separately, one might ask "What do many computer scientists think?" or "What views have many computer scientists taken away, after reading the paper and thinking about the subject?" or "How has this paper influenced the perspective of many computer scientists?" That's a separate question, with different answers, and potentially a bit more subjective. For instance, you might find that many computer scientists have formed the opinion that the Turing test is possibly the best way we have to formalize the informal question "Can machines think?" into something answerable in a scientific way, and that many computer scientists think that at least in principle it should be possible for machines to think, if we can surmount the engineering challenges (see the Church-Turing hypothesis).
You might also be interested in reading Human computing power: Can humans decide the halting problem on Turing Machines? and Would creating a complete computer simulation of the human brain prove the Church-Turing thesis? and https://philosophy.stackexchange.com/q/15460.