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.