Learn English – Research in the workplace reveals that people work for many reasons _______

I suspect this is a mistranslation of German bzw. = beziehungsweise, which can mean either respectively or or as the case may be. The translator has taken a passage in which the latter sense is intended and substituted the conventional abbreviation of the former sense.

The latter sense has no convenient one-word English translation, much less an abbreviation. I have often regretted this, because bzw. is so useful.

It sort of works, but not so gracefully, if you just substitute or for resp.

For each of these problems (or tools), we start by presenting the natural concern underlying it (or its intuitive objective), then define the problem (or tool), and finally demonstrate that the problem can be solved (or the tool can be constructed).

In short, there is very little difference, if any, and I wouldn't worry about it. Only as a noun ( e.g. until forever) should it always be written as forever.

The Oxford English Dictionary says:

Ever:

5b: in phrases, for ever (sometimes, esp. in U.S., written forever, q.v.)

Forever (adverb):

1. The phrase for ever (see ever 5b), written as one word. Chiefly U.S. exc. in sense ‘incessantly’.

2. quasi-n. Eternity, perpetuity.

I think most readers wouldn't even notice whether you used one spelling or the other. But the OED indicates some subtle, potential differences: it is spelled for ever everywhere and in all senses, but the spelling forever for the adverb is more common in America, whereas in England forever is more likely to mean "incessantly", so in a sentence that describes a repeated action. As a noun, it is always forever.