If you do do this, be sure to do it in a very very well ventalated area, because the gasses given off by both the paint thinner the the decomposing foam are not fun. Also, be sure to where gloves, resporator, and all that good stuff.
I'll second that, wear the Tyvac suit and a resperator. All I have to do is see white (Expanded Polyeurithane) and I want to caugh. Far too many shows and constructions before I got smart.
So far lots of ideas - green adhesive, or believe it's a form of contact cement a blue one that best bonds, otherwise there is lots of home center "panel adhesives" that are designed to stick foam to surfaces. Liquid Nails and other types of general purpose adhesives will at times work, and at times not - depends upon what lot number of construction adhesive you have. Some burn up about the foam, others stick to the foam really well. Could also spray foam adhesive the panels to a surface for a really good bond. Silicone being the next option probably won't work well.
Gorilla Glue as theory in doing foam should work well, so does 3M "Foam Fast" spray adhesive.
For shaping, the past I did sand paper by way of various disk or belt sanders, chain saws, grinder with chain saw blades, shur-form and rasps, Grandpa's meat cutting knife, an
electric knife, a hot knife, a very sharp paint scraper used as a draw knife, a table saw, blow
torch, spray paint, a variable speed
router and lots of other tools to shape foam.
As a starter, determine what form of foam "expanded polystyrine" - the white dots in a sheet or "extruded polystyrine" the blue, pink, amber and other colors of it. Both work well but at times what works for attachment and or shaping for one won't with another. The white foam makes for a more textured surface faster but the extruded types are easier to shape. Spray paint with them can make for just as much texture. There is other types of foam also such as would be used to make piers and floating docks. Beyond this, even the padding used in a sofa is foam (don't attempt to cut it with the table saw) it will at times work and can be shaped.
Spray paint is a curious thing that does not get along with foam. Sculptural Arts type coatings, Jesso - from an art supplier, and various
Rosco type coatings work well with foam, so in also texturing your surface would a spray paint primer. IT's another technique. Prime the surface, fill in holes and cracks, make the surface solid than paint as needed.
In coating, it's often a question of a hard surface in making the foam a solid, or a more rubbery coating that will allow for flexibility. Could be done both ways and there is various coatings out there that will get you the Audrie II type foam coated so it's a solid surface of plant or some others that are solid like plaster. Options abound. For a simple fireplace, one would assume just a primer be it spray paint or from
Rosco if not even Jesso would be fine.
Another coating could be a combination of plaster or paris, Sobo or other flexible white glues, and some joint compound. Should work well as long as the surface is not bumped much or much moving thus bumping around. Use only as much water in this compund as necessary to make the powders paste and if possible water down the glue rather than the plaster.