There is approximately 95 square miles in a hex. Each district is 1 square mile. Thus, you can have 95 districts before spilling out of the hex.
As a GM I would state that if you were spilling out of a hex you would need to prepare that district in an adjacent hex paying whatever preparation costs that district would have.
Additionally, if your city grew so large that it occupied most (or all) of the hex I would also say you could no longer have a Farm, Mine, or Quarry in that hex with the city. However, that would be a house rule.
You pay the same cost as if preparing the hex.
If your District Grid is full and you want to add another district (for example, if you run out of available lots in that settlement and want to construct additional buildings), you can create an additional district for that settlement by paying the preparation cost for the settlement’s terrain as listed on Table 4–6: Terrain and Terrain Improvements (see page 214).