You don't need to wash the yeast if you don't feel like going through the trouble. I use a sanitized jar and fill it with the dregs and trub. Then I seal it and stick it I stick it in the fridge until I want to use it again. I brew pretty often so the fridge yeast only stays there for 2-3 weeks. on brew day I pull it from the fridge when I mash, let it rise to room temp and pitch the top half of it when my beer is at temp in the fermenter. Sometimes it'll take a little longer to start up fermentation but it works just like a fresh starter. It also doesn't add any off or weird flavors to the brew.
As for adding sugar after primary fermentation you can do it for a couple of reasons and get some neat results. First is priming sugar which helps carb the beer if you bottle. Second you can dry out a beer like a saison by adding a simple syrup made with table sugar. Or you can add some flavors or depth by adding complex sugar syrups made with candi sugar, turbinado, or even molasses and honey. They will dry out the beer a little but you'll get some great flavors with them. Also by adding these sugars, except the priming sugar cause it's negligible, you increase the alcohol content created by the yeast.
