A1."People walk a long way."
A2."People walk long ways."
For this one, the A2 doesn't make sense to mean the same thing as A1. A2 means something like There are ways that are long, and ways that are short, and the people take the long ones. It wouldn't be used like this in normal speech, I think. A1 is correct because of a group of people are taking one road, for a long time. I think this is what you mean here.
B1."People live a happy life."
B2."People live happy lives."
B2 makes more sense in this case, because unlike in A, where many people can take one road, many people do not live the same life, they live individual lives. Both are grammatical and make sense in regular speech, however. You would say "One lives a happy life".
C1."People get water for daily use."
C2."People get water for daily uses."
This is a bit different, because both are correct but mean slightly different things. C1 means that water is used for general use every single day. Like, all the different uses all put together is "daily use" or "general use". C2 connotes that the water is used for specific daily tasks. Like People get water for daily showers and washing dishes. I'm not entirely sure why actually, but when it is singular in this case, it is more general than the plural, even thought they end up meaning the same.
D1."People get water for many use."
D2."People get water for many uses."
D2 is the only correct one here. "Use" can be used in the singular to talk about general use, like "put to good use" or "general use" or "daily use" or "weekly use". BUT since you use the word "many" here, you MUST use the plural, because there are many specific tasks that are being done.
I know this is confusing, and as a native speaker I had some trouble explaining. Please ask if anything is unclear in my answer.