don't know what you mean by "stone paver surround." Please describe what it is and how it works.

something like this

http://www.pavestone.com/blog/stone-grill-for-outdoor-living-how-to-build-one

The web site you posted has actual plans for building just such a thing. So why not use it/them?

For seeing different end results, just search Google Images.

While there may be other ways, common mortar could be used and would certainly work for leveling up the first course of stones and accounting for imperfections in the patio surface.

^^you're going to need a mortar bed, as Yard mentioned, both for stability and for leveling the first course (which is critical). So you do that and in a few years water gets in there and if you get winters, pops the joints and thinks start getting wonky. Making a kitchen from these has never made sense to me because interlocking segmental walls are designed to move - the last thing you want to happen under a $2000 piece of 1.25" granite.

If it were me and I had a good bit of cash, I'd do stainless steel cabinets from Danver (google it). If it were me and I had *my* champagne tastes/beer budget, I'd build a frame of steel 2x4s and cover it with concrete board. Redhed the bottom plate right to the concrete slab. That way you have the option of a stucco finish or any stone or brick veneer, which'll look better than the stone lego blocks.

seems reasonable - any instructions on how to do this so I can read up on it?