The answer to your question is:

(1A):correct

(2A): incorrect
(2B): correct

3.Suppose we dropped the depuis phrase. Would that change the answer? I.e. which of the following would be correct?

(3A) incorrect
(3B) correct

“depuis” in french is a time adverb “adverbe de temps”, it can be easily shifting or/and it can be removed.

4.If we were saying the same thing as 2 but in the present, which of the following would be correct:

(4A) incorrect
(4B) correct

5.If we were saying the same thing as 3 but in the present, which of the following would be correct:

(5A) incorrect
(5B) correct

The correct proposition (5B) is not in the present “au présent”. It is “au participe passé”.

The simplest way to write this sentence with the verb “meurt” in the present is:

(5B) Miss Ashburton malade, meurt quatre jours avant Noël.

replace the proposition: “après avoir été malade” by l’adjectif: “malade”

I agree with sapienz’s answer, I don’t think I need to write them again. I’ll try to explain it a little more.

You sentence looks more or less like this:

[subject], after [action1], does/did [action2]

If the verb for action2 is anything but future tense, action1 is always resolved, so can’t have present tense for action1 if you also have present tense (or past tense!) for action2.

Like you noted it your background, it has to do with the fact that there are two actions, one anterior to the other, so you have to show that.