Is Wall of Ice casting damage and frigid air damage counted by segment or only once?

Question

I am trying to figure out how exactly the spell "Wall of Ice" works. I am DM now and have been playing for a few years, but I have never seen spells of level 6 in action due to most games ending before this kind of spell becomes available.

Upon reading the spell description I have come to the conclusion that wall of ice is quite powerful against several enemies that may also be close to the caster's allies as they can place each 10 foot segment exactly where I want (so long as they touch each-other). However I am trying to figure out whether the caster can instead focus down one opponent by criss-crossing its square (and perhaps even the squares it can get ejected to) with walls. I am also trying to figure out whether they can use this spell to criss-cross a narrow passage and force pursuing creatures to take the 5d6 damage from frigid air for each segment they cross.

The wording of the spell:

You create a wall of ice on a solid surface within range. You can form it into a hemispherical dome or a sphere with a radius of up to 10 feet, or you can shape a flat surface made up of ten 10-foot-square panels. Each panel must be contiguous with another panel. In any form, the wall is 1 foot thick and lasts for the duration.

If the wall cuts through a creature's space when it appears, the creature within its area is pushed to one side of the wall and must make a Dexterity saving throw. On a failed save, the creature takes 10d6 cold damage, or half as much damage on a successful save.

The wall is an object that can be damaged and thus breached. It has AC 12 and 30 hit points per 10-foot section, and it is vulnerable to fire damage. Reducing a 10-foot section of wall to 0 hit points destroys it and leaves behind a sheet of frigid air in the space the wall occupied. A creature moving through the sheet of frigid air for the first time on a turn must make a Constitution saving throw. That creature takes 5d6 cold damage on a failed save, or half as much damage on a successful one.

At Higher Levels. When you cast this spell using a spell slot of 7th level or higher, the damage the wall deals when it appears increases by 2d6, and the damage from passing through the sheet of frigid air increases by 1d6, for each slot level above 6th.> If the wall cuts through a creature's space when it appears, the creature within its area is pushed to one side of the wall and must make a Dexterity saving throw. On a failed save, the creature takes 10d6 cold damage, or half as much damage on a successful save.

I am looking for clarifications on the following points:

1. If a creature is crossed by more than 1 wall segment, for example if an ancient dragon is hit by four segments as the caster tries to box it in. Does the target have to save and take damage vs each segment or only once from the wall as a whole?
2. If the caster forces a creature into a box that is smaller than the creature (again imagine an ancient dragon), do squeezing rules apply to the creature?
3. If the caster zigzags a wall across a 10 foot wide corridor or alleyway in this kind of shape: /|/|/|/ and the pursuers manage to somehow destroy the ice and attempt to pursue, will they take 10 times the frigid air damage (once for each segment) or will they only take it once per turn even if they cross multiple segments.
4. Do the wall segments have to touch each-other at the tip like this: /|/|/|/ or can the caster theoretically have shapes where one wall segment touches another in a T shape like this: |-|-|-|

I am tempted to rule these a certain way, however I would be open to any crawford tweets or erratas or just general input that could point me the right way:

1. No, each creature only needs to save once regardless of what kind of maze of ice you are drawing around them. Maybe I would consider giving the creature disadvantage if hit by 3 segments or more as it realistically gets much harder for the target to dodge in that scenario, but I am not 100% sure about that either.
2. I would probably rule that creatures do indeed get squeezed until they make it out of that zone (or break the walls)
3. My first reading gave me the impression this would apply only once per turn for the whole wall. However upon rereading I realised that "moving through the sheet of frigid air for the first time on a turn" in the relevant sentence refers specifically to the sheet of frigid air left behind by a single wall segment. To me this implies that each sheet of frigid air is its own entity and would trigger the damage individually. This would make sense to me as the caster in this case would sacrifice area covered to focus both the damage and the blocking utility of the spell. This would perhaps make the spell more of an option compared to the lower level and generally superior wall of force.
4. Contiguous would imply T shape is not acceptable to me as the way I imagine "contiguous" is by picturing the wall spreading itself at its edge, therefore this would be a valid shape: /|/|/|/ but this would not be valid shape: |-|-|-|

Answer 1

First of all, you have a small but significant misunderstanding on how you can place the sections of a wall of ice:

A wall of ice must either be flat or spherical

The spell's second sentence says (emphasis added):

You can form it into a hemispherical dome or a sphere with a radius of up to 10 feet, or you can shape a flat surface made up of ten 10-foot-square panels.

So you cannot make zig-zags, criss-crosses, or any other more complex shapes. Hence, you can't hit the same creature 10 times by putting them at the center of a 10-pointed ice wall star shape.

However, even if you could do that, the creature would still only be subjected to the damage once, because...

There is only one wall

The effect on the initial casting is described thusly (emphasis added):

If the wall cuts through a creature's space when it appears, [...]

Regardless of the shape, the spell only creates one wall—it's called wall of ice, not walls of ice. For each creature, the wall either cuts through its space, or it doesn't. It doesn't matter how many times it does so. Hence, the effect described can only ever trigger once per creature per casting.

Spells don't stack with themselves anyway

Even if it was possible to trigger the initial damage twice on the same creature, the effect still wouldn't stack, due to the rules given in the DMG for combining game effects:

But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap.

If a spell would apply the same effect more than once to a single creature, this rule guarantees that the effect still only applies once, since clearly the two effects have the same name (the name of the spell). (There are exceptions to this rule, but wall of ice is not one of them.)

There is also only one sheet of frigid air

This is a bit subtle. We have to read this section of the spell's text carefully (emphasis added):

The wall is an object that can be damaged and thus breached. It has AC 12 and 30 hit points per 10-foot section, and it is vulnerable to fire damage. Reducing a 10-foot section of wall to 0 hit points destroys it and leaves behind a sheet of frigid air in the space the wall occupied.

Despite the fact that each 10-foot section of the wall has its own pool of hit points and can be independently destroyed, the wall is described as a single object, and the sheet of frigid air occupies any space that was formerly occupied by the wall. Given this wording, I would regard any 10-foot sections of frigid air resulting from destruction of wall sections as smaller parts of a single sheet of frigid air that potentially spans the wall's entire space. As a result, we conclude that the damage from passing through the frigid air only applies to each creature at most once per turn.

In rare cases, a creature could be damaged twice in one turn

There is one situation I can think of where a creature could be damaged twice in one turn by wall of ice. If you ready a wall of ice and release it as an enemy is running toward you on their turn, they will take cold damage from the initial casting, and then they will have the opportunity to break through the wall with their action and then move through it with their remaining movement. In such a case, I believe they would be damaged a second time as they moved through the frigid air, since these are instantaneous effects (damage) that happen at different times, so the rules for combining effects don't apply.

Summary: each effect hits once per turn

I've written quite a bit above, but what this all boils down to is very simple: each damaging effect of wall of ice can affect a given creature at most once per turn. This is consistent with how most damaging spells work in 5e, and it should make it easy and quick for you as the DM to adjudicate the spell's effect in actual play.