The water must fit within a 5 foot cube, per the first sentence of the spell description. it's not 125 cubic feet in any shape, it's a bounding box.
This only determines the water you affect with the spell. It does not say anything about the spell effects being limited to this 5-foot cube, only the water you can cast the spell upon. You can stretch it out into ribbons if you like, since that's a simple shape permitted by the second bullet.
You can't take it with you. “Animate” doesn't cover moving it (think of animation as just a succession of new shapings in-place), and there is an explicit limit of 5 feet in the first bullet for how far you can move the water.
It can't affect ice or snow, only the colloquial, common, non-chemistry meaning of “water” that means the liquid phase. You can see this colloquial meaning used in the last bullet where it talks about how you can “freeze the water”. (Wouldn't make much sense to substitute “ice” into that bullet point, would it?)
You can cast multiple instances of alarm
The general rules say that if you know the spell, have the slots, have the components, and meet any additional requirements, you can cast a spell.
You can even ignore the spell slots if you have the ritual casting feature and take 10 minutes to cast the spell as a ritual.
Casting alarm multiple times does not violate any of those rules and it is not a concentration spell.
Spells use language to describe effects outside of the rules
If there is not a general rule that describes something, then the spell's effect must say it for that thing to be true. A spell says what it does. Nothing more or less.
Other spells have language that specifically says what happens if you cast it multiple times. For example, minor illusion:
The illusion also ends if you dismiss it as an action or cast this spell again.
This gives credence to the interpretation that there are no rules for casting spells multiple times since it had to be elaborated in spell descriptions. But also, it makes the lack of such text in alarm significant and meaningful.
Prestidigitation even specifically allows, but limits the recasting of the spell:
If you cast this spell multiple times, you can have up to three of its non-instantaneous effects active at a time, and you can dismiss such an effect as an action.
Presumably it was important to put that limitation in there because prestidigitation is a cantrip and thus has no limit to the number of times it can be cast (unlike alarm which is limited by slots).
Similar spell, also able to be cast multiple times
An example of another spell that can be cast multiple times like alarm would be glyph of warding. It is similar in many respects to alarm and also has no language restricting it to one use.
Alarm does not have any such language and no general rule says you cannot do it, so you can!
You cannot increase the size of the spell effect by casting at higher levels
The spell says (as you also noted):
Choose a door, a window, or an area within range that is no larger
than a 20-foot cube.
The spell will always specify if it has any effects that will scale with level or any other kind of details. The spell does not say anything about effects changing when you cast at higher levels so they do not change.
Ways to increase the effectiveness of your alarms
Using alarm in the middle of an open field and centering it on you while you sleep is not going to be the most helpful if someone is going to attack you for example. However, it is not useless and actually still could be helpful if the intent of that person was, say, to pick your pocket while asleep.
The clearest way to improve your use of alarm would be:
- Camp in a cave or tent and put the spell on the entrance
If you cannot find an enclosed campsite you could try any of these:
- Put the spell on the path leading to your campsite
- Place a valuable object obviously in camp and place the spell on it
- If you place the alarm spell only around you, try making the alarm audible so that even if they do get to you, your companions are also awakened
- Place alarm spells on all of your companions (audible or not)
- Blanket the area with many alarm spells
You can certainly cast alarm as many times as you want (make sure you are observing the casting time though), but really just picking a more secure campsite is going to be the best way to get better use out of alarm.
And it is important to note that alarm is a low level spell, it is not intended to solve all of your security needs. But in the right situation and with the right preparation it is invaluable.
Best Answer
Basic Area of Effect Rules
As far as Area of Effect goes...
The linked section goes on to explain exactly what each of the five basic shapes means, and none of them allow for shaping.
Shaping
One of the design precepts of 5th Edition is plain language - in other words, spells, features, and traits only do what they say they do. Take these spell descriptions for example...
These spells all create walls but have highly specific and different rules for how those walls can be sculpted. Two can float in the air at whatever angle you like (Light and Force), the rest must be touching the ground or a particular material. Some are constructed with panels of a particular size (Force, Ice, Stone), while others have a set size (Light and Fire). Some must be a flat plane or a sphere (Force and Ice), while others infinitely shapeable (Stone) or can do cylindrical rings (Fire).
It's pretty clear from just these examples that the rules for shaping a spell, when available, are specific to the individual spell. What holds true for one spell does not hold true for others.
Conclusion
One of the core concepts of 5E is exception based design. If something is supposed to be different from the general rules, it will say so - and the explicit exception wins. The general rules are covered in Area of Effect, and make no provision for shaping.
As mentioned earlier, another core concept is use natural language. If it doesn't say it can be shaped, it cannot be shaped.
Specific Example
The specific example, Alarm...
One proposed answer to the linked question suggests you can break it up in blocks. The spell does not say a certain number of cubic feet, or panels, or a ring, or anything else. A room is an "area" in plain language, so Alarm fill a room's specific shape, as long as that room is "no larger than a 20-foot cube". If you're outside, it could cover a smaller area (like a clearing) as long as that area is "no larger than a 20-foot cube". But turning it into a ring (squared or otherwise) - nope.