The only thing I can recommend is hi-temp silicone (the red stuff you can get at auto parts stores). We use silicone for all of our granite and marble installations. I'm not sure I understand how screwing into the wall will affect the venting. We just hung a 550 lb. stone shelf on a wall without interfering with the chimney behind. That being said, we hung this stainless steel surround on a wall mounted cleat made of Hardie Trim:

Not done by us, but you might like our selection! we invite you to visit: www.omegamantels.com, We do customise our product.Through a few pleasant and effortless consultations,We can definitely guide you in the process of creating your own cast stone centerpiece

Not sure of your style, but I like a stacked stone look. You can choose thicker stone for a more traditional look or go with thin similar pieces for a more modern clean feel. Also there are plenty of color variations that you can utilize as well.

I would take a diamond wheel on a grinder and abrade the shiny surface of the marble a bit. Cut some score lines into the marble. Use the wheel to widen the crack enough so that you can get thinset packed into it while you are applying thinset to the rest of the stone. The crack could be a crack that happened long ago and is no longer moving. You could apply a strip of Kerdi-band over the crack as you are doing your tiling. It "may" help. If it is still active movement, and your new tile cracks...then you know you have a separate issue to deal with, but I wouldn't worry about it at this point.