I do not think that this question fundamentally relates to formal and informal registers.
It is true that many "formal" documents contain complex sentence structures. Sometimes that is because the thoughts being expressed are complex. Sometimes that is because the thoughts being expressed will not bear critical examination. And sometimes that is ...
If answer D were
It WAS hoped that the virus would disappear soon."
then the tenses would match.
Since "is hoped" is a present tense expression about a possible future event, it should be used with "will disappear".
The words "would disappear" could be used if there were a conditional in the sentence:
I think [that] the ...
I think it's the "that" as a subordinating conjunction, and not the tense at all
D has a "that" which subordinates the dependent clause about hope. C does not have one to subordinates the clause about the map, which makes it less formally correct.
I published my first scientific papers in the '70s, so I probably represent an elderly and conservative view on this. However, I would not use an idiomatic phrase like "pinch of salt" in a scientific paper - though I'd certainly use it in an appropriate context, in a conference presentation. I expect to see formal language in a published paper. ...
Yes, both correct and suitable for formal occasions.
"The squad broke up because of how toxic they were. But I'll admit that I was toxic myself." Here you are using 'myself' correctly to emphasise or admit that you were one of the team's toxic members.
"Why are you yelling at me for not hearing the alarm. You didn't hear it yourself." - ...
Ask yourself "why do I want to use this formulation". If it is because this is the best, most clear and elegant way of expressing yourself then you can leave it in. If, on the other hand, it is just because you want to demonstrate that you know an English idiom, then leave it out.
You will need justify the claim either way. The expression means ...
There's nothing wrong with using a more casual idiom or two, especially in the abstract or conclusions section where it can help to present your point of view concisely without interfering with the presentation of the facts.
For example, Estimating the reproducibility of psychological science, a fairly high-profile article published in Science, doesn't shy ...
"What brings you here?" is neutrally phrased and wouldn't be considered impolite in any scenario I can think of. I'd probably use it in a formal situation if I just wanted to know why the other person was there.
“I can’t stress enough” may sound a little pushy, or perhaps even desperate.
I prefer your idea of using the word “fit” in place of “appropriate”.
So I think something like this would work well:
I really do feel I’d be a good fit for this position.
And mostly importantly, you’d then explain why.