Mastic can be used as an adhesive in non-wet areas. Your drywall is obviously in good shape, which means by itself it's not being hit by or incurring standing water. You didn't mention and water staining or degradation, so sure, mastic can be used to adhere the tile to it.

Grid lines: It will most certainly help to add layout lines on the wall. It might help to strike chalk lines, then use a straight edge and sharpie marker to go over those lines. With differing tile sizes, you are correct in that you use the layout grid lines for overall guidance to keep the overall layout looking good, but on a tile-by-tile basis within the grid lines, the tile spacing is adjusted plus-or-minus here and there to keep that overall pattern looking good.

Regarding uneven tile sizes...you might want to do a rough mock up. Your goal will be to not have a larger-than-normal tiles adjacent to several other larger-than-normal tiles. Several large tiles in a row can really throw the layout off. Same with several smaller-than-normal tiles in a row. That can result in a run of wide grout joints. Try to work out your layout and installation so larger-than-normal and smaller-than-normal tiles are mixed and mingled throughout the layout.

Mastic usually holds tile pretty well on the wall, it's usually a "no sag" installation unless the tiles are heavy. If you think your tiles might sag, then have a collection of tile spacers and/or tile spikes (spacers shaped like wedges) to prevent sagging. These can be store bought or home made.

I'd clean off the backs of the tiles. Use a sharp chisel to shave the dollops of silicone off the tile. If you start with crap, you'll end up with crap. Why start with compromised materials?

If you use the "premixed adhesive" (mastic) to set the tiles, wait several days before grouting. Mastic cures by drying, so it needs air.

If you use the "premixed grout" which is also a mastic-like material, read the installation and cleanup instructions. It can shrink as it dries, so it might not be the best choice if you have wide grout joints as the excessive shrinkage could result in it pulling away from the tiles.

If you decide to opt away from the Mapei premixed stuff, see if they have Mapei Kerabond and Mapei Keralastic. That combination gives good working time and good stickiness in terms of minimizing sag.

Mongo

Can I (should I) tile right onto the sheetrock?

Yup.

Should I apply backerboard over the sheetrock?

Nope.

I know I was reading in Bill's FAQ that he doesn't recommend premixed adhesive for most applications, but I was wondering if it would work for this one.

Okay-- time to get serious. :-) Premixed thinset (or mastic) has a very specific use, and that's for ceramic tile (8x8 or smaller) over sheetrock (or cement board) in dry areas. Under normal circumstances, this would qualify. But you're using a handmade tile, which most oftentimes is notorious for not being flat, which means you'd have to build it up some with the mastic. Not a good idea. In this case, you'd be alot better off with a portland cement based latex modified thinset (Something like Versabond from Home Depot, or Ultraflex II from Mapei)

Should I use spacers or should I do something like using chalkline to create a grid and center the tiles in the grid? We're going to have pretty large grout lines (probably 1/4 inch or more) and it seems to me that the grout lines will have to be uneven to make the tiles line up correctly. Does that make sense?

It makes perfect sense. I would suggest going to www.tile-experts.com, and look for a product called "Tile Spikes". The come in assorted sizes, from 1/16" to 1/4", and as the name suggests, they vary from front to back, so you can adjust them as needed. You can also double up spikes if necessary in order to keep it straight. And yes, I would strongly recommend the use of a chalkline.

Can I leave the silicone stuff on the tiles or do I need to figure out a way to remove it or "rough it up?"

I'd want to remove it, not because I disagree with what the salesman said about enough area to bond, but more because those "dollups" might end up making the tile stand proud from the rest of the backsplash.

Thank you for the replies and excellent advice! I'll work on removing the silicone and finding the right supplies for the job.

Thank you again for your fast replies and great help.

Jenmna