My rough calculations estimate that around 50 million litres of water must be stored at all times to sustain the station for at least a month in the event of a failure of some sort.
I believe that the "one month of storage" logic is not correct. A space city will be utterly reliant on its technology working properly. There are so many things which would require technology, water, atmosphere, day/night cycle, thermal management.
Here on Earth, if the machinery keeping our cities alive broke down people would be dying in droves. Water, electricity, gas, petrol, telecommunications, we are super reliant on them working smoothly and having excellent uptime.
Although I wouldn't dispute the usefulness of a buffer, and 50 million litres does seem reasonable or a bit on the generous side.
Redundancy and decentralization
On a space colony, the best way to manage the processing of atmosphere and water would be to do it with hundreds of parallel units all of which are capable of working independently, that way if a unit or three fail there is no danger to the colony.
Decentralization could be taken to the extreme by having each dwelling have its own independent water supply and recycling. This is not nearly as extreme as it may seem at first glance. These days Air Conditioning window units are a common sight on the sides of buildings. One function they can perform is dehumidification, which with the right engineering can produce drinkable water. An appropriately designed unit can easily produce 15 gallons (60L) of water per day, this is rather more than the minimum amount of water a person needs per day (according to UN standards) and is a reasonable daily usage for someone on a rainwater (rather than townwater) scheme and so practicing frugality in water user.
The idea of using dehumidifiers or other condensing methods to draw water from the atmosphere introduces the intriguing concept that a space colony might not even need plumbing for water, or another way of looking at it is can use the atmosphere for plumbing. It sure eliminates a whole lot of pipes and pumps and if any single unit breaks down that unit is very easily repaired or replaced. There is a reason the small window units are popular these days and it has a lot to do with it being the most economical approach - it's cheaper and easier to mass produce 20,000 small identical units than a single big custom built unit and it is by far the more robust solution.
Is using the atmosphere for water buffering and storage crazy? Not at all! The atmosphere of the Earth contains a lot of fresh water.
The atmosphere contains 12,900 km3 (3,000 cubic miles) of fresh water, composed of 98 percent water vapour and 2 percent condensed water (clouds): a figure comparable to the renewable liquid water resources of inhabited lands (12,500 km3).
The water cycle is vital to the functioning of Earth's biosphere, so the idea of using a mechanically-augmented water cycle rather than having pipes running everywhere is certainly not complete madness. In this case, the primary mechanical augmentation is using dehumidifiers in place of rainfall. To a certain extent humidity is self-balancing, evaporation is faster when humidity is lower, so a few lakes might help with passively maintaining balance, but it would be wise to invest in active central climate control which is responsible for either adding or removing water from the atmosphere.
How much water could the atmosphere hold? That depends how big it is of course. The area is stated at $50 sq. km.$ and a cubic km of air at 20C and 50% Humidity contains 10 million L of water, so if the height of the atmosphere was 200m ($10 cub. km.$ of air) the atmosphere would hold 100million L of water which would seem to be a pretty solid buffer.
Of all challenges, I think that waste recycling is one of the greatest.
If we are going with an augmented water cycle approach which minimizes the need for plumbing, the obvious solution is to use evaporation extensively and return water to the atmosphere as quickly as possible, a common technique to reduce the volume of waste is to just evaporate off the water using heat and fans. This is quite a popular design for toilets in remote locations, the urine and excrement simply falls into a pit, where heat (passive solar and/or heat from decomposition) and a fan (solar powered) evaporate off the water, and the solids decompose. I'm not saying that exact design would be good, just that it scales well.
Removing the water isn't too hard, but the solid component of human waste is more problematic, the low tech solution is essentially a wetland, let microbes and plants recycle the waste back into water, CO2 and N2. Plants are great at pumping water into the atmosphere so this can double as an evaporator. The main problem with an approach like this is that it requires considerable space and plants are terribly inefficient at utilizing light, but you may want a wetland as part of the city for aesthetic reasons.
A related way to close the water cycle is to have waste water from residences go not to a wetland but instead to agriculture where it nourishes useful crops, and the plants return the water to the atmosphere. This isn't quite as easy as it sounds because it is also desirable to grow crop plants under tightly controlled conditions, but it would definitely be a feasible solution.
The high tech solution to waste disposal is to use an electric plasma arc to directly dissociate the molecules (plasma pyrolysis) then release the resulting gases to the atmosphere. Human waste is moderately energy rich so this process can generate rather than consume energy and might actually be the less energy intensive solution to disposal of solid waste. It's a sterile solution which would go well with intensive forms of agriculture which aren't compatible with organic farming styles.
Water Use Reduction
The most water-efficient way to grow plants is aeroponics (growing plants with their roots dangling in a mist of water and nutrients), any kind of plant can be grown using aeroponics and it works in microgravity too. Compared with conventional agriculture water use is dramatically reduced.
For animal protein, smaller animals are more efficient than large ones, at the extreme many insects are capable of growing using humidity in the air alone.
For personal hygiene, I've seen some interesting ideas in science fiction, including using ultrasound to clean skin by knocking off particles of dirt and dead skin. Ultrasound is already used in beauty care so it is a real thing. I suspect many people will prefer water even if only as a form of recreation/comfort, but as noted earlier the water usage for someone on a rainwater scheme is very reasonable and wouldn't be difficult to provide. There are toilets which don't rely on water, but a simple way to economize on water is to re-use shower water for toilet flushing.