An infinite plane of oceans and ice with a pangea or multiple continents rising up from the parts in the middle. The sun and moon are mere spectral lights in the sky with no weight. Without a sun, moon, or rotation, how might tides, winds, currents, and other things like that work on it? Would it have any at all?
Hm, this really depends on how 'realistic' vs 'fantasy' you want to get. If we're going strictly by real-world laws of physics, wind in a place without rotation or a star to heat the atmosphere would not exist on a world like this. That said, if you want to lean more into fantasy - perhaps some forgotten celestial deity created this realm, and the sun/moon have no weight, but do emit their own light and heat? If the celestial deity could create artificial wind, and some kind of force of magic keeps the wind rotating, well... that could solve the problem! Of course, I'm sure there are plenty of other fantasy based solutions to it. Just an idea that came to mind!
I'd say that if your already dealing with an 'infinite plane of oceans and ice', then physics is already out the window, so just go ham with it. you needn't be so concerned about astrophysics in a setting which is already fundamentally fantastical. Personally I dont think there needs to be any explanation for how the wind works, or the tides- if you have some idea related to that then great! otherwise, just move on to some other worldbuilding.