Learn English – ‘Enjoy the rest of your day’. What is the name for such expressions

Unfortunately, no. However, the French phrase bon appetit is very widely known, and you can use that as an alternative.

A very informal option would be to say Dig in!, though this has the connotation of eating sloppily or in large amounts, and doesn't necessarily carry the idea of enjoying an elegant, modestly portioned meal.

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".