3
"Put [x] to the test" is an idiomatic way of saying that you are submitting something to a process of testing. Even though "the test" uses the definite article, it refers to the process rather than a specific test, so that may involve one or more tests.
Your second option with the indefinite article is not as idiomatic. We would normally say that we put ...
2
Yes, the sentence does require an article before the word Japanese. It's because we don't talk about team.
We talk about a team or the team. The choice would depend on whether the writer thought that the intended audience were familiar with Samurai Blue. If yes, then use the definite article. If no, the indefinite. If unsure, use either one.
And the ...
2
With most acronyms, you have to think about how they fit into your speech. If you feel that the acronym is actually replacing the words it stands for, then use, or don't use articles as you would if you were saying the name in full.
"CIA" is a proper noun - it is the name of a government agency. You would normally say "the Central Intelligence Agency", so ...
2
An actual answer is a reply that answer the question instead of going around it. The actual answer is the correct reply.
Let's say a politician was bribed. I ask him "were you bribed?". If he says "my finances are none of your concern", that is not an answer to the question. If he says "No", that is an actual answer to the question, but a wrong one (a lie)....
2
No 1. is overwhelmingly the most natural to me (British English).
No 4. is grammatical and natural, but has a different meaning: it assumes there is a Tesco in the vicinity, and asks if it is over there.
1
You generally use the definite article the when you are referring to a specific thing and both you and the listener/reader understand which particular thing you are talking about. This is the case in the answer that you referred to: the answerer is talking about "all of the air surrounding the planet".
When talking about a thing in general, we don't use ...
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