SHORT ANSWER:
Yes, the continuative present perfect may be used to signify a state which continues right up to the present regardless of whether it continues in the present. It is not, however, used to signify a state which does not continue right up to the present.
LONG ANSWER:
The 'continuative' present perfect establishes the past event or events it names as a state which endures right up to the present.
Situations grammatically depicted as states are presumed to continue indefinitely, until something happens to end them.
Consequently, the present perfect permits you to infer that the state it describes continues in the present. In fact, this is the default assumption with an unqualified present perfect. If you had only the statement “I've been driving a hearse for the last 25 years” you would legitimately infer that he is still driving a hearse.
But the present perfect does not entail—logically require—the continuation. Linguists call this an implicature, as opposed to an implication: it is in inference which may be cancelled by a contrary fact. That's what you have here, with the statement “Today is my first day driving a cab.”
Note, by the way, that there is in this particular use of the perfect, no difference between the use with the progressive, “I have been driving”, and without it, “I have driven”. The phrase “for the last 25 years” imposes the same continuative reading on both.
Note, too, that because the hearse-driving does not continue into the present the speaker might with propriety have employed the ‘simple past’: “I drove a hearse for 25 years.” I suspect he uses the perfect (and the progressive) because what he wants to convey is that there is a continuity in his activity: “I’m still driving, what’s changed is that now I’m driving a cab.”
Note, finally, that the notion of ‘present’ is defined pragmatically. Obviously when someone says he has driven a hearse for 25 years he does not mean that he drove continuously throughout that period. By the same token, the ‘present’ which that driving continued ‘right up to’ is not the moment in time when the statement is uttered but “today”
The case of John’s tardiness is a little different. In the circumstances you describe, neither the continuative present perfect nor the phrase “for the last 30 minutes” is proper. You are dealing with a much different timeframe and scale than the cabdriver. Your answer (“alas”) makes it clear that you are pragmatically defining three distinct epochs: 1) you wait for 30 minutes 2) you depart, and a couple of minutes elapse—long enough, at any rate, that you are no longer in the vicinity of the appointed meetingplace 3) then John calls. Consequently, the state of waiting (1) did not continue “right up to” the present (3).
Here are some ways you might express the facts:
I waited for you for thirty minutes, but, alas, when you didn’t show up I left.
I waited for you for thirty minutes, but, alas, I’ve left now.
I waited for you for thirty minutes, but, alas, I had to leave.
You should not employ the progressive I was waiting here; that is employed to speak about something which happened while you were waiting.
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."
Best Answer
There would be possible ambiguity with, for instance:
In that case you might be speaking about how long it will be until you do the task, or the duration it will take you to perform it. You're talking about the future; either is possible.
But your sentence is past tense:
So, no. Your interpretation of "We did the task after 10 minutes passed." is not "possible". "in ten minutes" needs a reference point of "now"...and to be read as "ten minutes from now" you must be using present tense.