"coiner" - one who counterfeits coins. Not something we hear of much today, but in earlier times was a reasonably familiar sort of criminal.
"box-room" - a room in a house (usually a small room) which is just used for storing things, usually things that are not wanted very often. The collocation "box-room attic" is unusual, because these two words mean nearly the same thing. (Not quite, because a box-room could be anywhere in a house, not just under the roof).
"cistern": yes, it is still quite common for British houses to have a water-tank in the roof space - sometimes two (hot and cold). This was partly to provide a head of pressure for taps and showers, and partly to guard against interruptions in supply (and in the case of hot tanks, to provide a reservoir of heated water for when you needed it quickly, as in a bath).
There is not a literal tunnel, it is saying that between the tank and the sloping roof there is a long and narrow dark place (dark because it is behind the cistern).
"of course" is a parenthetical remark meaning "as you already know", or "as is obvious". It is much more common in speech than in writing, but of course this writing is meant to suggest somebody is speaking, and telling a story.
"For" says that the sentence is a reason or explanation of what precedes. So the meaning of "For of course he was thinking .. " is something like "(He was excited) because, as you probably realise, he was thinking ... "
All the links you cite should have been either "Tell us what you think" or "Let us know what you think" (one of them even has the correct title, but is wrong in the first sentence). Getting confused, and ending up halfway between the two, is not uncommon, but it is not right. (In my opinion, it never will be right no matter how often it is used: but it is definitely wrong now).
Best Answer
First question: "Last night" is perfectly normal English for "yesterday between 5 p.m. and midnight" (night time). Yesterday night is something only non-native speakers of English would use.
Second question: There should be no problem understanding that "last night" means yesterday night. If your friend had meant that it was her last night in NYC because she was going to move somewhere else the next day, she might have said my last night in New York. OTOH, she might have been using shorthand (headline English), which is not unusual for photo captions. Her communication problem rather than your comprehension problem.
Third question (unasked but latent, nascent, and imminent): "At New York" is not idiomatic American English. It has to be in New York.