Walking through the hall of the police station hall, Brunswick notices a familliar face in a sideroom.

When he gets over his excitement, Brunswick briefly considers why the great crime reporter of the Daily Clarion, the “Policeman’s Friend”, Harry Jupiter, is downhere in Brighton.

When eventually he puts two and two together, Brunswick is overwhelmed withand thrilled by the idea of Jupiter writing about him.

On his arrival at the police station, Jupiter made a series of requests—as expected from him given his character—personality- such as having a room for his ownmself and a typing machine.

Right now, finishing off his piece for tomorrow’s paper has the precedence over aneverything else.

When he finishes with it, he must obviously turn back to the piece on Crystal’s murder case.

Thus far, Jupiter has conceived* only the title: “The Blood on the Plush.” Which, he dulyAnd he asked for Peplow’s** opinion.

*or is it better to say “has come up with”?

Come up with is more informal.

It's not a misspell of "people".

Good to know.

When he eventually he puts two and two together, Brunswick is both overwhelmed withand thrilled by the idea of Jupiter writing about him.

On his arrival at the police station, Jupiter made a series of requests—as expected from him, given his character—such as having a room for his own room and a typing machine.

Right now, finishing off his piece for tomorrow’s paper has thetakes precedence over aneverything else.

When he finishes with it, he must obviously turnmust go back to the piecework on Crystal’s murder case piece.

Thus far, Jupiter has conceived* only the title: “The Blood on the Plush.” W", for which, he duly asked for Peplow’s** opinion.

It's not a misspelling of "people".

When he eventually he puts two and two together, Brunswick is overwhelmed with thrillexcitement by the idea of Jupiter writing about him.

"overwhelmed with thrill" is grammatical but I think really unusual. He can be thrilled, or could maybe "feel an overwhelming thrill". And I think it's permissible to put "eventually" where you have it, but it sounds much more natural here.

On his arrival at the police station, Jupiter made a series of requests—as expected from him given his character—such as having a room for his ownmself and a typing machineewriter.

Or "a room of his own".

Right now, finishing off his piece for tomorrow’s paper has the precedence over anything else.

When he finishes with it, he must obviously turn back to the piece on Crystal’s murder case.

Probably "return to" or "come back to" is more likely than "turn back to".

Thus far, Jupiter has conceived* only the title: “The Blood on the Plush.” WAbout which, he duly asked for Peplow’s** opinion.

I think "conceived" is acceptable, but "has come up with" is a very natural expression and probably better here.

Technically what I've done here is an error - it should be one sentence, "the title, about which he asked" or "the title, which he asked about". But in my opinion this error is stylistically appropriate here and as a native I'd be very comfortable saying or writing it.

**Peplow is a man and a friend of Jupiter's.

It's not a misspelling of "people".