mjhjmtu

I have a planet that is tidally locked to its sun.

The ocean is shallow (a few hundred meters) and was artificially created in the past by harvesting the system's Oort cloud or outer-system ice asteroids (machines that autonomously operated over centuries to re-direct ice bodies at the planet) – a terraforming process I'll call "ice bombardment".

Backstory: This world was created for a utility purpose (1 of hundreds), and over the centuries has been abandoned (political or economic powers have long-since shifted). The pretext is that large interstellar ships were sea-vessels, as opposed to "parking" in orbit. It is not hard sci-fi, but the biggest "handwavium" in the story is economics (the Great Wall and the Pyramids were built even though the economics don't make sense). None of this backstory will be discussed.

I realize a tidally locked planet will have a low magnetic field (if any), and this ocean will eventually evaporate. I need water covering the planet, except for a glacier on the "north" pole. The glacier is large enough that its weight has uplifted a scattered ring of small islands.

Is a glacier possible on a tidally-locked, shallow-sea planet? What kind of atmosphere/weather conditions would the planet allow on the sunny side? I have researched tidally-locked, ice, shallow-sea, and "eyeball" planets, but I'm not sure I can have mostly ocean and a glacier too (it seems logical to me but I'd rather be sure).

Bonus question: could I allow for bio-engineered oxygenation? I don't want a perfect atmosphere, it is intended to be an artificial world in decline.

The problem is that the planet is tidally-locked. So you have a perpetually-lit (and hot) side and a perpetually-dark (and frigid) side.

The atmosphere on the perpetually-sunlit-and-hot side will be continuously evaporating water from the liquid sea...then depositing that water as snow on the perpetually-dark-and-cold side.

That cycle does not seem sustainable, since there is no mechanism to return that frozen water to the daylight side to replenish the liquid sea. Eventually, the planet will have hot desert on the sunlit side and vast frigid glaciers on the dark side.

Some glaciers (or, earlier, sea ice) on the dark side will push into the twilight --very slowly--, producing a trickle of meltwater, but not nearly enough to replenish the sea. However, that depends upon the local topology -- in many areas, glaciers (or sea ice) may instead flow farther into the dark side.

from OP: /a terraforming process I'll call "ice bombardment"./

Ice bombardment continues.

If this method could create your ocean, it could maintain your ocean. The terraforming process accumulated many more ice asteroids than were needed at the time the planet was built. The surplus were left along the orbit of the planet in a rough ring. The terraformers distributed them so they would come down through the atmosphere at predictable intervals, replenishing the planet with space rain.

I do like @user535733 idea of glaciers forming on the dark side and pushing their way into twilight. Have that too, for sure.