While conquering and developing the entire galaxy (huge), I noticed that the game caps research and income production at 32,767. Additionally, any attempt to produce more than 32,766 units of food immediately turns into a negative number your population begins to starve. Lastly, the maximum technology score you can earn is 262. Does anyone know if these limitations were intentional, or if there is a patch to remove them?

Seems like the programmers simply did not expect anyone to exceed these numbers and used signed two byte integers to store the values (older games, being far superior in quality to the modern day rabble, as all GOGers know ;) used a lot of optimization methods like this in order to reduce memory consumption). So you are simply getting an integer overflow.
The technology score cap on the other hand seems to be something within the rules of the game, or maybe a bug.