Sand and clay. At a craft shop, you'll be able to find some clay that must be fired to keep its shape. Do not use self hardening clay. You can experiment with adding water to the sand/clay mix or just mixing the two ingredients without to see which works best. The reuseable clay/sand mix will dry, holding the sand in place. Soak your whole construction to dissolve the mortar when you want to reclaim the bricks.
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You could try a flour and water mixture. I would say that depending on the exact mixture it could be a good mortar and should be dissolvable (or at least not too hard to clean off). Another option could be to use modeling clay or play-doh. It all depends on how strong and temporary you want it to be.
I've never seen it. I presume cake icing won't do. One of the "play dough" variants might...
What do you mean mortar? Mortar and pestle, or like the military mortars?