My vote is always for re-use (except the trash pieces, which can still be used as a filler). For your question of using a single layer of brick (I assume you mean vertical layer for the walls) -- bad idea without lining it with steel or firebrick, and a quick way for people/things to get burned. You can also use two layers spaced with an air gap or filled with loose or crushed rock (and you can use the trash pieces as well so you don't need as much rock). You will want to mortar the bricks (mortar), not stack them, and you'd need a solid base. I'd recommend using this information from The Family Handyman as a fairly good guide.

Otherwise, build a proper firepit and use the bricks for a walkway or as a flat area for standing/seating around the firepit. I'd suggest knocking off the larger chunks of old mortar with a rock/brick chisel.

You can build the basic structure with these bricks, then line the fire pit itself with fire bricks. That's how fireplaces are made.