There is plenty of water in the Alps, even the "Tote Gebirge" has water if you do enough research. Some stretches I had to carry more water than normally but I never had to carry more than 3L (2L Platypus type of container integrated into the backpack and 1L sport-bottle to easily grab on my belt) most of the time I only carried 1-2L and usually had 500ml or even 1L by the time I reached another water source. I drank from all rivers that looked OK and didn't bother to filter (and never had problems). I wouldn't do the same thing in Sweden or Finland but considering the population density it really was no issue. Also I made a habit of asking people who I would meet about any knowledge they had about water.
Hygiene was easy since I left at dawn (4-5 AM in summer) and was still above the tree-line when it got dark, I just used whatever I could find (streams, lakes, or just those things where livestock drinks out of - don't know the word in English). Also I couldn't wash myself every day I managed to clean myself pretty decently like this at least 2-3x/week at least. And a hot (or cold) shower every 7-10 days when I found one. (The huts sometimes have coin operated showers which was pure luxury for me). I also had a small bottle of anti-bacterial soap I used 2-3x/day on my hands.
Going to the loo was more of a challenge. I hated the idea of leaving anything behind, including my own stink, (and a lot of the frequently used trails are littered enough with toilet paper as it is). I usually dug a small hole so I wouldn't leave anything behind. My philosophy was that "if somebody knew I was there I had made a mistake". Also being a total coffee-addict served me well up there because I was able to control the timing of my bowel-movement with having a strong coffee in the morning (brought some instant coffee powder and just mixed it with cold water for this purpose ... sounds horrid but I wouldn't have been mentally able to survive without it :))
[1] this was overkill, but the idea was that there would be no way I was going to eat this unless I would be in real trouble. I was told that this is what people in Canada recommend to bring to survive long stretches. No idea if that is true but it made sense. In retrospect the pemmican had the same effect, but was slightly better in taste than the smell of cat food (and also why I opted to feed the dog with pemmican instead of giving him my cat food).