These are two words that have baffled me for long. Dependency is given as 'excessive dependence' in Chambers, but I would love to know how the spoken usage is. My guess is dependency has a political touch to it. In addition, there is an independency as well in the dictionaries, though it does not sound popular.
In common usage, infrastructure often is used unqualified to refer to good physical conditions in a community (as, for example, "Our town has the infrastructure to support your robot factory!"), although it implies little or nothing about tax, economic, and labor conditions. Of course one can also say "Their infrastructure is awful!"; that is, "good" is not an inherent quality of infrastructure.
Note, infrastructure is "The basic facilities, services and installations needed for the functioning of a community or society."
Regarding linguee.com, their "About" page clearly says, "there is no other technology anywhere else in the world that compares with Linguee", so obviously you should keep using it. :) They also assert that the translations they provide (which, if I understand correctly, are in this case English to German) are human-made (or at least human-moderated). In comparing the English and German, it seems that the connotation you suggested for the German word (i.e. "conditions necessary for a business idea to work out") do not hold up in these translations; for example, "worst imaginable conditions" going to "denkbar schlechten Rahmenbedingungen".
The general principle here is just that the focusses on a specific instance of something, whereas a implies one among many possibilities.
Thus in #1, the reduction of mercury pollution implies either that it's just one example of a type of pollution that could be reduced, or that mercury pollution is a clear example of things you might spend $1.5 billion on. But it's optional regardless of the exact sense intended.
In #2, if the hours of darkness are few implies we're specifically talking about how many hours of darkness there are at the time/place of fasting. There's no special grammatical rule applicable here, but idiomatically I'm sure most native speakers would include the in such contexts.
In #3, a range of techniques simply implies that the writer isn't concerned with exactly which range of techniques he's talking about. If in fact he meant the particular techniques actually used by his company, for example, he could have said our range, More rarely, in contexts where he's thinking of the complete range of possible techniques, he might use the definite article. But it would be generally considered "ungrammatical" to have no article at all in this construction.
Note that these are very fine nuances that won't normally apply anyway. In all the "articles" I've looked at above, and in comments below, any of definite | indefinite | zero article could be used, and it's unlikely many if any variations would strike most people as "odd".