1. You want a 5 to 1, sand to Portland cement mix for your deck mud. If you'll look in the Shower Construction thread in our
Liberry, you'll find various ways to achieve such a mix. You could also use one of the proprietary mixes, such as the MAPEI 4 to 1 mix you mentioned, but I think you'll find a plain sand/cement mix with no additives easier to work with exactly what you want for your mortar bed.
2. If you can ensure the firebox will never again see a wood fire, the mortar bed will be fine in that area, too. I think what you currently have must have been a mix using fire clay for it to have held up under wood burning conditions.
My opinion; worth price charged.