What adhesive can I use to reattach and seal these fractured tile pieces to my fireplace?
I've had a similar situation and I found Liquid Nails for Marble and granite to work very well. It's also rated for use on metal. You can purchase it in single tubes and it's great for spot repairs on tile and granite. Just make sure the surface is cleaned and follow directions. Be sure to secure the tile in place until it dries.
I couldn't tell if there is grout between your tiles. Grout is prone to crack with vibration but I'm sure you'll want to match whatever is there. If you change what's between the tiles it may not match. If there is a gap, be sure to use spacers for a uniform gap on each side before you grout. Then all you do is match the grout color.
You can also use the Liquid Nails to join the pieces of tile before you mount them but if they are large pieces and the surface you're mounting it to is even you may not have to do that. Good luck.