1- I sat there, still waiting, being worried that she would never
arrive. (... and I was worried ...)
This is grammatically correct, but awkward. We would normally say "worrying" or "worried" rather than "being worried".
1'- I sat there, still waiting, worried that she would never arrive.
This is fine.
2- I was preaparing the food , my friends being sick of waiting. (I
was preparing the food and my friends were sick of waiting)
This absolute construction doesn't really mean that the speaker was preparing the food and that his/her friends were sick of waiting; rather, it suggests that the speaker was preparing the food because his/her friends were sick of waiting.
By the way, there should not be a space before the comma.
2'- I was preaparing the food , my friends sick of waiting.
This is awkward at best, though it's hard to explain why. Absolute constructions with adjectives do exist, but they're not quite as flexible as ones with participles. Instead, you could say something like:
With my friends sick of waiting, I had no choice but to go prepare the food.
3- Being shocked by his death, I passed out. (When I was
shocked by his death...)
This is very awkward; I could imagine it in a book from the 1800s, but not in present-day writing (let alone speech).
Honestly, in present-day writing I would expect simply:
I passed out.
since the context should make it obvious that the speaker was shocked; but if you really need to drive home the point with a modifier, you could write:
Shocked by his death, I passed out.
as you suggest.
4- The word “book” has a double meaning , the noun form being “ a
set of pages inside a cover”, while the verb form is "to arrange to
have a seat etc. at a particular time in the future"
The word being is fine here, but there are some other problems.
Firstly, "has a double meaning" does not mean "has two senses". (And book actually has many more than two senses.) But maybe I'm misunderstanding the intended context of this example?
Secondly, the noun and verb senses aren't distinct forms.
Thirdly, it's a bit odd to speak of "the" noun and "the" verb when there's been no indication before that point that there exist one noun sense and one verb sense. (Though this is mainly an issue because in reality there exist many senses; if there were really exactly two senses, I probably wouldn't blink at "the noun sense" and "the verb sense".)
Lastly, there are some formatting issues with the punctuation.
So this should probably be something like:
The word book has multiple senses, including a verb sense meaning "to reserve in advance" and a noun sense meaning "a set of written, printed, or blank sheets bound together between a front and back cover".
4'- The word “book” has a double meaning , the noun form “ a set of pages inside a cover”.
This doesn't really work.