Komnos, you problem is too much farm plots for the amount of farmers and seeds you have.
Set all but 1 of your 9x9 fields to fallow for ALL SEASONS.
Make sure your farmers are set to ONLY do farmer tasks. I set mine to Plant fields, Collect Plants, and Harvest Plants, because I like my farmers to thresh and go out into the great wilds to grab wild plants when I screwed something up and am getting low on plants... But they don't do anything else, so they will do farm type tasks as soon as possible.
Make sure you set the (o)ptions - harvest to only farmers harvest. A trained farmer harvesting will get a lot more food then random unskilled or low skilled dwarves.
a 9x9 plot is really too big for almost all forts. Early on, a single 3x3 or 2x4 will keep you well stocked in a year round plant (ie, any above ground plant or plump helmets). Add small plots of similar size when your fort starts running low on plants in a couple of seasons, and you'll find food isn't a problem anymore--- booze is.
Good luck!
For irrigating, I use bucket brigade method (see the dwarf wiki entry
irrigation) or use floodgates and fill chambers. If you make a "fill chamber" that is 1 tile per 6 tiles you want to irrigate, then you don't have to worry about over filling your new farm room with water. To do a fill gate irrigation, build a small chamber between the brook/river inlet tile and your farm room. Put a second door or floodgate on it, so when you pull its lever, it opens, and allows the contents of the fill chamber to flow into the farm room. Put a flood gate on your river/brook inlet, hook it up to its own lever, breach as desired. Now you can let your fill chamber get full, close the inlet, and then open the fill chambers gate/door into your farm room. Perfect amount. For LARGE farm rooms, I usually add a single tile to my fill chamber to make up for the water that will evaporate while the water floods into the room.
Pro tip: When breeching into a river or brook, if you build a door one tile back from your floodgate (or door), you can safely breach the water source without worrying over how long it might take a dwarf to come along and flip the lever to close the new inlet's floodgate/door.
Bucket brigading and draining a small pool are very quick and easy ways to create a muddy room. Using floodgates and doors hooked up to levers is more dwarvenly to me, so I personally like to use that method when it isn't too inconvenient.