... you can't present perfect (or continuous) and past simple within a sentence.
As it stands, this rule is incorrect. In many cases it is acceptable and logical to mix past and present references in consecutive clauses
I lost my keys last week, but now I have found them.
This makes sense: A was true then, but B is true now.
This, however, does not make sense:
He has decided to go hiking, so I went hiking as well.
This sentence amounts to A was true then, because B is true now. The simple past describes a past event, your going hiking, but what the present perfect describes is not a past event, his decision, but a present state which is the result of a past event--his state of having decided. That present state cannot be the cause of the past event. The cause must be either a past event or a past state:
He decided (event) to go hiking, so I went hiking as well or
He had decided (state) to go hiking, so I went hiking as well.
The important thing is not to mix time references illogically.
As for the sentence in your friend's email:
Getting that email was such a pleasant surprise, because I was just thinking how I've been wanting to send you an email
There is no mixture of time references here, because the progressive construction "I have been wanting" marks a state, not an event, which may very reasonably be taken to continue into the present out of a past which is marked (by "just") as immediate. In effect, these pasts inhabit the same time frame as the present.
In any case, the "rules" are very loosely applied in informal discourse; see my discussion here. A casual email, which your friend probably dashed off in excitement, should not be held to the formal literary standards of coherence.
This is a somewhat archaic construction. The more modern way to say the same thing would be
It took the prince three days to die.
In my mind, the "was [timespan] dying" construct does serve to emphasize the fact that the person was dying the whole time, rather than "working up to it" in a sense.
(And just to be perfectly clear, yes, it does mean that the prince is now dead.)
Best Answer
"John got a mentor to guide him throughout his life" implies that the act of acquiring a mentor was a single event that took place in the past. It says nothing about the length or status of John's life in the present.
"John got mentored on a daily basis", taken in isolation, implies that John is no longer being mentored on a daily basis; the mentoring stopped at some point in the past. (In a story being told in past tense, however, it would not necessarily carry any such implication.)
Taken in concert without further context, the two statements form a tiny story told in the past tense and can be read either way. If you want to make it clear that the mentoring is ongoing, you would probably want to switch tenses and say "Now he gets mentored every day." However, the use of the past tense only implies, at most, that the mentoring has stopped, not that John's life has stopped. (Perhaps he couldn't afford the mentor, or perhaps he learned everything he wanted.)