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You can combine field the same way you combine other type of building (placing 3 or more fields next to each other). The production will combine plus 2 bonus and extra foods depends on how many field more than 3 you combined. 

For example combining 3 fields each with 1 food production will make larger field that produce 5 food (1 * 3 + 2). But combining 5 field each with 1 food will results in 9 food (1 * 5 + 2 + (5 - 3)).

Another way to produce food is using fish pond that will appear every 5 connected water blocks. Fish pond produce food every day depends on number of houses surrounding it.

Also thank you for reporting bug, it should be fix now.