First, about the plants: evaporation could plausibly be in a range more, less than, or just the same as it would be in open water. Many real-world plants increase evaporation by exposing so much leaf area. In other words, whatever you want it to be.
The ocean should have some sort of top-to-bottom circulation or else whatever marine animal life there is will consume all the oxygen in deep waters and the lower levels of the ocean will become completely anoxic.
Next, assuming there's some sort of equilibrium in the water cycle, at least as much water has to fall as rain, somewhere, as evaporates from the ocean. That means that humidity levels have to reach 100% at least some of the time, over part of the planet. If the air is sucked dry of moisture by mountain ranges, etc. before it reaches the remoter regions, it's possible that it never rains on much of the planet.
If rain does fall everywhere, it's implausible that water in distant areas can find a path to drain all the way back to the ocean. The alternative is that there are inland salt seas, along the lines of Great Salt Lake in Utah, here and there. Your "ocean" might well be considered just the largest of these.
The Earth's weather is more or less divided into latitude bands--certain latitudes where it rains a lot, others where deserts occur. This is driven by long-term continental-scale convection patterns where rising air creates rain and falling air doesn't. Your planet might have the same thing, in which case all the clouds and rain only happen in certain horizontal bands around the planet.
Or maybe your planet's water cycle isn't driven by rain after all--isn't it kind of a cop-out to assume the planet is like Earth in every other way? There could also be a geological water cycle in which water circulates through the planetary mantle and crust by plate tectonics, trapped in rock layers, and your ocean is the only area where it reaches a liquid form. Mars is suspected of having enormous amounts of water trapped beneath the surface as ice. You could also plausibly create a system without a steady equilibrium if the planet is geologically young and its ocean is fated to last for "only" a few tens of millions of years.