What is the climate and weather of the aquatic biome?
Environmental conditions do change in the oceans, but the terms climate and weather are not usually applied.
In the atmosphere, climate is longer-term changes in rainfall, temperatures, humidity, pressure, winds, etc., while weather is short-term changes (days to weeks) changes in the same factors.
in the ocean environments, temperature and pressure play important roles, but pH and salinity are also important factors. Needless to say that humidly in the oceans is not a factor as it's 100% water!
Every marine or lake organism evolves over million of years to fit into a given environmental niche. If the environment is fairly stable, the environment will continue to thrive. You can think of long-term marine environments as roughly the same as "climate" on the land. If environmental changes happen rapidly, like say El Nino, this might be analogous to weather.
During El Nino or La Nina events, vast schools of fish migrate to areas of the oceans that have the right temperature for them to thrive in. When things settle down again, they migrate back. A hurricane on land/surface of the ocean can also have big short-term impacts to the shelf regions of the oceans too - you could argue this is "oceanic weather."
Organism evolve in certain temperature/pressure/salinity conditions but when those conditions changes (like they are now with global warming) species are challenged to adapt or die out. Right now corals are struggling to adapt to longer-term changes in the ocean temperature and ph conditions, brought on by atmospheric above land climate change.