or is it just me?

I do what she asked & there is no piece on completion. If I go back to Shinwa, she prompts to go back to same quest giver for piece 1 I I

Did you do an account search for Piece 1? Sometimes it can accidentally get quickstocked elsewhere and you don't realize it, but then they won't give you the piece again. I just tested as well and it's functioning for me. Shinwa doesn't give you the pieces, the quest givers do when you complete a quest for them (just making sure since you mentioned she isn't giving them to you, but you need to give them to her):

Making them easy to account search for you :)