Learn English – Is the expression “Say your piece” or “Say your peace”

When you say "mind" you are saying "be aware of" or "be careful with" not to be confused with "beware of".

They might overlap, depending on why you may want to be aware of something. You might need to "mind the dog" because he bites or you might need to "mind the dog" because you are about to absent-mindedly step on it's tail.

"Beware of your head" is strange sounding. "Mind your head" means to be careful with your head. "Beware of" in this context implies that your head is going to do something bad to you, whereas "mind your head" is meant to say be careful not to let something bad happen to your head.

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".