As for Princess Astrid's jewellery, it is an interesting topic indeed. The photo with the velvet band choker was, as Knightship say in the reply, taken at the Gala Performance held in connection with the Spanish State Visit in 1984. Pinned to her dress she is wearing the Breast Star of the Spanish Order of Isabel the Catholic which both she and her husband (and at that time Crown Princess Sonja) received at the beginning of this visit.
Unfortunately I do not know anything about the choker or the diamond element on it.
I tried to write an entry about this visit on my blog and if you are interested I will add the link to follow should you want to have a peek. I would be very happy for any feedback on it:
As for the second photo Princess Astrid is indeed wearing a Turquoise choker. I have seen a photograph in colour (though of not very good quality), so it is definitely Turquoises. As you say, it also makes sense as she is wearing Queen Maud's Turquoise tiara. Not only that, but she is also wearing the not so often seen large Turquoise corsage pinned to the turquoise coloured top of her gown.
The photo was taken at the State Banquet hosted by King Olav V in 1973 for his young guests the Queen of Denmark and Prince Henry during her State Visit to Norway.
Again, I tried to add some information about this first day of the State Visit on my blog here: