... 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.
The present perfect tense, as you asked about, is when Event 1 (your parents opening a restaurant) happened at an unspecified time before Event 2 (your present conversation).
The reason that there is obfuscation and confusion is because of "a few weeks ago".
If you had just stated "The most important news is that my parents have opened a restaurant.", it would be clear that the perfect tense is appropriate because Event 1 was completed at an undisclosed time before Event 2.
"a few weeks ago" adds definiteness, but not exactness.
For example, if you stated "My parents opened a restaurant two weeks ago.", it is clear that you could not use the perfect tense with a definite time.
That being said, it is my opinion that you giving a time frame for when the restaurant opened has removed the indefiniteness of time, and you should not be using the perfect tense.
Have a nice day.
Best Answer
1.I've just bought a book on English grammar, and it looks pretty good.
This sentence used a present perfect with "just" which indicates buying a book occurred very recently. It can even mean you bought a book a few minutes ago.
2.I just bought a book on English grammar, and it looks pretty good.
This sentence is very close to No.1 in that you used "just" for the past tense.
The purpose of Both No. 1 and No. 2 is (1) to indicate the timing of buyig the book and (2) the fact that he/she has it now.
3.I bought a book on English grammar, and it looks pretty good.
Reading this sentence, you cannot tell whether the book was bought recently or not. It happened in the past. No. 3 is different from No. 1 and No.2 in that sense.