You know what I think?
Inklings can turn into squids at any time by essentially modifying their molecular structure to become a squid made out of pure ink with a shell in the shape of a squid.
when in human form, the ink is contained inside a shell that looks like a human body.
My theory is that Inklings are made out of substances similar to acid and alkali substances, which is why both of them die when coming into contact with each other, acids neutralise alkalis and vice versa, this also hints to why inklings die when they come into contact with water, water also neutralises acids and alkalis.
When inklings fall into water ink starts to leak out from their bodies before they evaporate, which could be the shell (their body) being dissolved and neutralised and the insides leaking out. Since there is constant exposure to the water when an inkling falls in, death is almost imminent. When an acidic inkling is hit by an opposing team's alkaline ink, the alkaline substance starts chipping away at their shell, which is why you see patches of opposite ink everywhere on the body, even when just standing in a puddle of the stuff.
Swimming in ink gets rid of the offending acidic or alkaline ink quicker than normal because you're neutralising it immediately by submerging it in the opposite element instead of waiting for the body's healing process to sort it out, it's like soothing a burn wound by coating it in water.
As for the swimming in ink part, remember how I said that the human form and the squid forms are merely shells containing the true entity of the inkling (pure ink) inside the body, well when an inkling wants to swim, they break the shell and completely become one with the ink, like pouring a glass of water into a bathtub, it blends in and you can't see it, just like the inkling! This also explains why there's so much manoeuvrability in a liquid that barely covers the ground (and walls)
When the inkling wants to become human again, they just reassume their forms and assemble their shell (notice how before they become fully human their body is made completely out of ink)
Now, about the whole thing on dying and respawning, I believe inklings bodies behave in a way identical to Master Core of the Super Smash Brothers series. For those of you that don't know, Master Core is a giant mass of swirling shadows that can contort his body into many different forms, all of this is possible with the centre, or the heart of his body. Which is a small core. You know that little soul that flies off when an inkling's body is destroyed? That's the core, that's the TRUE inkling. That's what gives the inklings the power to become human, squid, create shells and gives them life and most importantly, respawn after being torn into a million inky pieces.
Notice how this soul is visible to EVERYBODY, whether it's your soul, the soul of your teammate or an enemy's soul or even an Octoling's soul. You can see the soul of everybody who's splatted, making this something that's visible and probably tangible to an extent. If you were to destroy somebody's soul, that would be pretty bad. This is probably the same for the Inklings, meaning that if an Inkling's soul is splatted that would mean permanent death. This is why it's impossible within the boundaries of the game to target an inkling's soul. The turf war organisers absolutely forbid it since it would be murder. You are only allowed to incapacitate, but not kill...
Well, I think that covers everything!
TL DR:
I love you very much and I want you in my life, [username], will you marry me?
REAL TL DR:
Inklings and Octolings are made of Acid/Alkili like substances that neutralise (kill) one another when they come in contact with each other. This is also why water kills. The human and squid forms are merely shells that dissolve when they are neutralised, Inklings cannot be truly killed unless that little soul that flies off is destroyed, which is why you are prevented from targeting it.
