Grammar – Which Sentence Is Grammatically Correct and Why?

A. Working took place in the past. (A period of time is implied, of course, since you had to work for a period of time, but that fact isn't specified in this tense usage.)
B. Similar to A, but working took place over an unspecified period of time in the past.
C. Working took place over a period of time in the past. The tense specifies that there is a time also in the past that the period ended. (In your sentence, "until" is the wrong preposition; "before" is correct. Also, "before today" must imply "before your termination today"--which it does--to be correct.)
D. Working took place over an unspecified period of time in the past. My answer to C also applies here.
E. The person is still working here, and you want to know when he started. This isn't consistent with your scenario, so presumably that's why you don't feel comfortable with it. :)
F. It would be correct if the person isn't yet seeing his employment as being in the past. ("I have been working here for six years, and I'll be darned if I give up my job without a fight." would be an obviously correct usage, for example.) Once the person understands himself to be terminated, he had been working here for six years (when he was terminated).
G. Yes, I agree. "for the past six years" (or more often "for the last six years") should be used as "I have been working here for the past six years."

I disagree with Ekn.

"For the first few days" implies that something was going on continuously for days. While technically you probably thought about other things during those first few days, like eating and going to the bathroom, it is metaphorically valid, and certainly better in a literary since, to say that it was continuously ongoing. I would absolutely vote in favor of using "for" here.

However, "in" is not invalid. It says to me that at any time in those first few days that you attempted to figure it out, you couldn't, but not necessarily that you did so a lot for those first few days.

So both are valid, but in the context of a breakup I would use "for".