1) It depends what style barleywine you're trying to make. The traditional examples are from London and Burton-on-Trent. I wouldn't try to emulate exactly a town's profile. I would use distilled to get your carbonate down to an acceptable level for a pale ale. That said, you'll have so much flavor in that beer, the water shouldn't make much difference.
2) I usually wash my yeast when I reuse it. Google "how to wash yeast." I've pitched onto a cake before, but chances are you've got way more yeast in there than you really need, plus all the trub from the last batch. If there is too much yeast, the yeast may not reproduce to get acclimated to the new wort. You want young, healthy yeast, not old tired yeast. Having a couple generations grow in the wort will help it get acclimated to the higher sugars and probably will attenuate better, instead of the old yeast going nuts for a few days, dying/flocculating, and leaving your beer too sweet. The times I've pitched onto the cake, I got massive blowoff in the first few days, it got really hot, and then I ended up with a slightly stuck fermentation.
3) I've only mixed yeasts when I didn't have enough of one for some reason. I could see mixing a hefe yeast and a belgian yeast for a wit, or something along those lines, but 1056 and 1728 are similar (and neutral) enough I doubt it'll make a difference.