How did the DS9 crew buy anything at Quark’s without money?
One of the set decorations on the sound stage where the "Quark's Bar" was, was a mock ATM machine. It got moved around a lot. One of the buttons was labeled credits.
If the system I suspect is in place, the the food and drink served at Quarks to Starfleet and their dependent is charged to people's financial accounts, Quark would likely have a business account the funds would be transferred to. I think it reasonable that Quark would need to have a way of making long distant payments without having to physically ship GPL to suppliers.
Or, Starfleet eats and drinks for free, this is in exchange for Quark not paying rent. Which means that Quark from a certain way of looking at it is in fact paying rent.
3) They're giving a incomplete description of the Federations economic structure.
Correct: they didn’t mention the foreign credit accounts. Because there’s little time to explain it to Lily in a den of Borg, and everyone one DS9 and Voyager already know about them.
But what you said doesn't go far enough, because it doesn't account for the observed use of money within the Federation, by people whose planets are Federation members.
That's the trick, both Picard (and others) statements that the money is gone
has to exist side by side with money still being there. This is where the
"incomplete description of the Federations economic structure" comes in. Because if both are
equally true, then something is going on beyond simply "there's no money," or "they only use it with outsiders."
Paris said money disappeared in the late 22nd century, he clearly use the word/term money. Then in the mid 23rd century money use is repeatedly referred to. One possibility is that the non-existence of money wasn't working the way society theorized it would and money was reintroduced.
Another possibility is that Paris's use of the word money had a special meaning that wasn't all inclusive.
If Paris solely meant money in the
physical sense disappeared, this would establish a particular meaning of the word "money" that other 24th century Star Trek characters could also be employing.
This would allow Picard to make a purchase while on vacation, and still honestly being able to state money no longer exists.
Monetary value that exists solely as electronic financial record-keeping in the Star Trek universe is not
thought of as "money."
When Riker encountered the piano player he could have had money in his financial account, but not "money" on his person.
I'll admit that this theory isn't perfect, but it will work with the
majority of the cases of money being mentioned.