Again, a medieval economy is not an industrial one. In the 1800s, there was plenty of urban demand for food that rural farmers could cash in on, but in medieval western Europe we're looking at roughly a 97%/3% rural/urban divide. With that kind of imbalance the average rural farmer would not have the opportunity to sell off a significant amount of excess crop. The opportunities for an individual serf to profit off of increased productivity simply weren't there.
By the late medieval period, sure, there was somewhat more robust intercity trade. But that's approaching 1000 years after the fall of the western Roman empire, which is stretching it if you want to claim cause and effect.
2. Cities can not sustain themselves but need the existence of villages that would sell them the food.
In the late medieval period farmers absolute would sell the surplus for money on the market. We also see also traveling merchants that would go from village to village to offer wares.
> Sell it to their neighbor, who is also a farmer and grows all the same things?
Some people in a village did not have land but were craftsmen like the iconic blacksmith.
An yes it was a development and early medieval period ages the serf was probably just happy to have slightly more to eat. It didn't all happen over night. Villages started very self-sufficient. Basically producing everything they needed themselves while we see much more diversification of labor later on.
3. I made a comment about the US South as well. An yes, history is not linear. There are just general tendencies.