Aren't fresh water deposits renewed by the water cycle? I have recently watched the documentary &quot;How Many People Can Live on Planet Earth?&quot; with David Attenborough. In it, the main factors that will limit total human population Earth can support are named. One of these was the limited amount of fresh water. There also was a part where it described how fresh water is distilled from astronaut urine on the International Space Station  .
My current understanding is that all the water (fresh or not) in nature (i.e. on planet Earth) is infinitely going through a water cycle, and thus non-fresh water is sort of distilled into fresh by this natural process.
My questions are:

Where am I wrong in my assumption about natural water distillation (i.e. is rain water not as clean as it should be in theory)?
Why don't we collect rain water (at least for plant watering, if it is not suitable for drinking)?
Theoretically, after an animal has consumed some amount of water, say a glass, how long will it take, after that animal urinates on the ground, for that water to go through the water cycle and become ready for drinking again?
Rain water is still one of the most cleanest water sources available. There may be some ancient underground aquifers that have clean uncontaminated water.

One issue with rain water is that atmospheric moisture - part of the water cycle - needs to condense on aerosols in the atmosphere before it can develop into rain. With the amount of pollution humans are dumping into the atmosphere some of that can form the aerosols that eventually develops into rain thus making rain water dirtier than it used to be - such as acid rain being formed when sulfur dioxides are dumped into the atmosphere when high sulfur coal is burned in power stations. Other aerosols include salt from the oceans.

The other issue with rain water is that the soil in water catchments can be contaminated by pollution. Rain falling on the catchments can absorb some of the contaminants thus making the rain water in the resultant catchment dirtier that it might have been in the past.

Regarding the rate of urine production of animals, it depends on the type of animal. A mouse will process water at a different rate to an elephant or domestic live stock. It is also influenced by circadian rhythms for each type of animal.