I have book about crystals, and it most looks like chalcedony, but I'm not sure, I don't know how much chalcedony is transparent.

Agreed it does, indeed, look like chalcedony.  

Dear Mr.Sorrow,
I suggest you change your name atleast to Mr.Happy.
According to you picture 'a' it looks like polished turquoise in cabochon cut.
but in your picture 'c' it looks like Smithsonite in cabochon and in your pictue 'b' it is Hauyne, I feel it is dark blue in cabochon.
the chemical composition is Na6Ca2Al6Si6O24(So4)2.
RI-1.50, RD-2.4-2.5, HARDNESS-5.5-6, CRYSTAL GROUP-CUBIC, CLEAVAGE-PERFECT, FRACTURE-UNEVEN, TENACITY-BRITTLE.
Found mostly in Australia, Germany, Italy, Morocco, Spain, Sweden and united states.

it looks like chalcedony, but it could be blue quartz. in the first picture it looked like it could be Peruvian opal. it is beautiful though.

It looks like a Blue Chalcedony  and the style of jewelry is something from one of the asian countries or from the southwest US.
In your next to last picture it look like it is a semi transparent stone which can be either of the two. Most agates have some matrix to them this is sort of a streaking effect like in Turquoise you see black lines this is the matrix of that stone, the agate will usuall have a matrix sometimes almost the same color or darker than the overall color, where as the Blue Chalcedony do not have a matrix and is a almost even color and your looks real close to the Blue Chalcedony due to the even color of the stone.