A) Nearly nothing is explained in any kind of manual (even the strategy guide is, for my opinion, of little value). You have to spend many hours reading through forums event to find out what military hospitals do (to know what the bonus to it does). There are at least lots of bonuses given by techs that are not explained. How should I make a decision what to research? I can't event deduct the use from visible effects as an 1% bonus to something might be hardly noticeable if you don't know what to look for!
The old V2 manual and strat guides are both quite out of date, but the AHD one is fairly informative with regards to the changes it had. But yes, manuals have always been something of a weak point for Paradox.
B) Terms are chosen suboptimal (e.g. at least in German the tech increasing your factory throughput is called a type of "efficiency". But it does not make your factory more efficient!)
That's questionable; throughput IS a type of efficiency. I usually divide it into 'time efficiency' (throughput) and 'material efficiency' (input/output changes). VRRP uses the terms 'throughput' and 'efficiency' pretty much interchangeably, which to my mind makes no sense either, but really, there's little point in quibbling over terminology.
C) Screens show misleading numbers (see link above for examples), e.g. the Trade Screen showing what your people want to buy regardless of what they are able to pay for. You find youself trying to satisfy a mostly virtual need. There are cases where a populous unciv colony can give you numbers 10 to 100 times higher than what people will buy in the end (if you play a country with a small population in its 'states'). Not to mention screens that show numbers that I recognize as wrong ( though there might be something I don't know that makes the number right ... see 'B' above for that)
No, the trade screen doesn't show what people want to buy regardless of what they can pay for. Let's try to get this very, very clear, as I've stated it over and over again in this thread and about a dozen others - Demand and Real Demand are separate values in the game, and you are not shown the one which shows total possible world demand for an item in the retail version of the game. The Betas DO see that number in addition to the 'real demand' that the retail version displays, and it is massively higher than you will ever see in the retail version. If you wish to see 'desire', then go into a savegame and look at the 'demand' figure. That is maximum demand in the world. 'Real demand' in the savegame is what you are presented with in-game as 'demand', and that's a vastly smaller number. Check some of the Modder's Heaven market reports to see the difference in scale between these two numbers.
There is NEVER a situation in the game where a populous colony will give you demand numbers 10 or 100 times higher than they can afford to buy. In fact, the more populous a colony is, the less likely it is to suffer distortions, since only very small POPs cause distortion and a very populous colony by definition DOES NOT HAVE small POPs. This is why d=!d traps are almost always less than 10% of the total demand for a good, and rarely go over 1%. There's no such thing as a 'mostly virtual' need, and there hasn't been since 1.2 was released. Please, please, PLEASE stop saying that there is, as it's a patently false, amply disproven hypothesis (one that I came up with in the first place, incidently, and then went on to disprove as well) which merely muddies the waters on what's actually happening in the marketplace.
There are certain cases of interface bugs which provide misleading numbers; production and trade have almost none of these left anymore. You're pretty much seeing exactly what's happening in the game in those areas now. Population is the main culprit here, with the old migration/pop growth bug etc.
And yes, the manual could be better; the same can be said for all Paradox games
I remember HOI1's manual which contained almost no useful information about how to play the game, but did have lots of interesting historical facts in boxes about how Rommel owned three cats. Vicky 1's was even worse in that regard, tbh. The V2 documentation is far from perfect, but is still leaps and bounds ahead of where Paradox were even for EU3.