How far will my summer truffle and water go?

13 grams to serve pasta for two is generous, but not extremely so. I think you're smart to keep the dish simple, you don't want to complicate things with extraneous flavors to muddle the taste of a star ingredient so special. Despite the very topical and interesting link provided by SAJ14SAJ, I'd be wary of sauteing the truffle in anything truffle flavored, even if it was 100% genuine (which most truffle products are not). If I was using truffle for the first time, I would want to be sure that I was actually tasting the truffle, not an additive designed to taste like truffle. I do like the idea of giving the truffle a light saute though, I'd just use butter or olive oil. If you do saute, you don't want to waste a molecule. Give the pasta a bit of a swirl in the pan used for the truffle to wipe up any of the precious oil left in the pan. Save a bit of the truffle raw to give the final dish a garnish of truffle shaving, if even just to taste it both ways.

As far as the water, it's worth a shot. How about making mushroom risotto the next day using the water (or more likely, brine) in the broth component of the risotto? Not knowing exactly what it's going to taste like, I wouldn't use it for your special dish. If it negatively affects risotto, at least you haven't lost much in the way of expensive ingredients.

EDIT: Oh, I'm jumping to the assumption that your truffle is black and will therefore stand up to sauteing. If it's white, don't cook it, just shave it over the dish.