¿Qué significa I heard that "in what circumstances" means "whatever circumstances are". Is it true?
And are there any other phrases using "in what" like this? ?

See a translation

“In what ___” is simply the question form of “in this ___” or “in that ___.”

Any phrase that works with “in this ___” or “in that ___” can become a question with the words “what” or “which.”

Ex:
“In this country, there are two major political parties.”
“In which country are there two major political parties?”

“In this situation, this device is helpful.”
“In what situation is this device helpful?”

“You’ll only encounter this kind of problem in these specific circumstances.”
“In what circumstances am I going to encounter this problem?”

This format also works with other prepositions besides “in.”

“We aren’t going to start at that time.”
“At what time are we going to start?”

“He was arrested on the grounds of (for the reason of) assaulting a neighbor”
“On what grounds (for what reason) was he arrested?”

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This format is considered the “formal” and “professional” format. In casual speech, the preposition (in, at, by, etc.) might be put at the very end of the sentence, or removed entirely.
“What situation will this device be helpful in?”
“What circumstances am I going to encounter this problem?”