So there's a planet that is used as a farming world (food) for its system. This planet has a single, Mediterranean sea-sized ocean on it and lacks any other major surface oceans (he hasn't excluded rivers and lakes). Is there any way, given these parameters, for a water cycle that is vigorous enough to sustain farming exist in this world? Can the balance of temperature from day to night in this world be maintained without any surface oceans to balance things? I'm having a hard time figuring out how this planet can work as it's written.
The water cycle is maintained by the abundant plant life
For there to be somewhat abundant water but no major oceans, there needs to be another place where water collects. This could be a porous layer of rock covering all the lower altitude areas of the (very flat) world.
The native plants would then likely have very deep root systems to access that water and bring it up to the leaves, where it would evaporate during the day as a way to cool the plant. (Days would be hotter and nights colder on a world without oceans). The evaporated water will form clouds, which protect the plants somewhat from the cold during the night.
This makes sense from an evolutionary perspective because the circumstances are very different. On Earth, water shortages are more pressing than temperature variations, so plants have pores that can be closed, fatty layers and of course the ability to shed leaves when there is no water.
The plants on this world would have none of that, because of the essentially unlimited water supply and advantages of daytime evaporation cooling.
While the temperature swings will be higher that doesn't make it impossible to live on. The areas of Earth that are the farthest from the ocean are still inhabited and certainly could be so with even more swing. You might not be able to grow terrestrial crops but local life could have evolved to survive the swings.
The water cycle is another matter--the only way I can see for this to be viable is if there's something that causes far more evaporation from that small ocean than Earth experiences. Perhaps that ocean is really a huge rift valley, complete with gobs of vulcanism. Note that this would make the water unsurvivable for land-based life.
I'd say that depends on many aspects. Planet size, farming amount, amount of people living there. If the planet has a thick atmosphere and is hot enough and the air around is very moist, water could be drawn from the air and used for farming. The colder poles could contain the ocean water. Also the temperature drop from day to night would be minimal with a thick atmosphere.
Perhaps this world has undergone at least some degree of terraforming. If this is a farming planet, efficient irrigation can make up for any shortcomings in the water cycle, including drawing up water from subterranean caches. Temperature regulation can also be addressed with use of solar reflectors in orbit.
There are other ways for a water cycle to work, the first that comes to mind being that most of the water is trapped just below the surface, thus allowing wells to be dug and used for irrigation.
Part of answering this would be to know what vegetation is like naturally on the planet. Presuming the inhabitants are native, they could only farm if plants existed naturally, so they would likely expound on whatever natural principles the world uses.
If the inhabitants transplanted from another planet, I would expect they would have technological capabilities that might allow it, and would have brought seeds from plants whose growth requirements they would know.
With enough topsoil and soil water to form a reservoir and enough plant life for evapotranspiration you could have a reasonably normal water cycle, somewhat similar to the Amazon Basin where water evaporated by the forest during the day falls back to earth in the evenings in a continuous semi-closed cycle where the average elapse time for cloud water is measured in hours.