Answers:

> Is 'Respektiere' in the imperative?

Yes, sort of, at least that is what it means. It is the *[Jussiv][1]*, a replacement form for imperative that uses Konjunktiv 1 as the verb form.

Jussiv is a bit archaic nowadays and not very often used, at least not in everyday conversation. Imagine the King asking his servant to serve wine, he would have said:

"Schenke er mir Wein ein"

Which is the same construct, or a typical excerpt from a cooking recipe that tend to start with "Man nehme ..."

>What case is 'jeder' in (e.g. nominative, dative)?

Nominative. Pull it in front to see why: "Jeder respektiere...". Also see next answer why it needs to be.

>How does 'jeder' contribute to the sentence?

It is the subject of the sentence.

>What does the whole sentence mean?

While the jussive mode is typically expressed in English with something like "let's", for this specific example I would rather choose a form of "to be to":

*Everybody is to respect the situation he is in: This will help everyone.*


  [1]: https://de.wikipedia.org/wiki/Jussiv