marble

Hi everyone. We had our fireplace opened up recently and a second hand marble mantelpiece fitted. The mantle shelf has been fitted slightly higher than the surround, which has left approximately a 10mm gap. Builder tried to fix it with some shims and caulking on the sides, but it's all visible...

I want to tile over an out dated marble surround (see picture). I was planning to scratch the old marble and then PVA. Then use a cement based flex adhesive to fix the new tiles (see picture) And advice greatly appreciated. It’s a small area but realise these small tasks can turn out a lot...