1) 20,000 cups isn't much. Said Galaxy class ship (assuming the original 4-5,000 man crew and not GRs asinine downsizing) would go through about that much in a day.
1,014 wouldn't, especially if only a third of them even drink coffee (on average, that seems to be the proportion in any large social gathering, using my church group and sporting events as a sample). So call it a seven hundred to a thousand cups a day, give or take, and that'll give you a little less than a month's supply of coffee for that little 2kg container.
To supply, say, a 10-year mission for that thousand-man crew, at that rate of consumption, you would need 366kg of caffeine. Which would basically fill four of these barrels:
Which speaks volumes as to the efficacy of replicators, doesn't it? Because ll the OTHER shit that goes into ten years worth of coffee is equally compact when you reduce it down to base molecules and strip the water from it. And in anhydrous storage, most of it can be vacuum sealed and sterilized so it'll stay good for DECADES, totally inert, until you plug it into the replicator system for use.
And all that is before you consider the advantage of waste collection and recycling. Human waste contains a lot of the same basic molecules as human food; if you have a system for sifting through all of that, separating useful molecules and storing them away, you can stretch that food supply like crazy and only use the inert bulk matter to make up the inevitable losses.
No idea, I don't own any tech manuals
I do, and that's exactly what they say, in almost exactly those terms.
TBH, I'm pretty sure early TNG implied direct conversion of energy into matter, which as has been pointed out, makes each replicator a potential nuclear weapon.
I figure it's kinda like how otherwise perfectly intelligent people keep telling me that CRTs and GPS satellites have to account for relativistic effects in order to work properly. It's a pervasive myth, but it's one that gets a lot of traction because alot more people THINK they know how these things work than actually do.