ferment
The word ferment means a commotion or excitement. Consider that the fermentation that turns juice or grain into alcohol is the result of the agitated development of bacteria, and then you can better appreciate the word's meaning.
foment
Stand outside the school cafeteria passing out flyers with nutritional details on school food, and you may foment a revolution — foment means stirring up something undesirable, such as trouble.
Yes, but you could also say something along the lines of "He fermented the opposition" implying that he started and developed it. I agree however that people will use ferment when they mean foment.
I'm curious by OP's phrase "agitated development of bacteria". First of all it's not bacteria but yeast, and second you don't agitate the solution after adding yeast. In fact you leave it alone and let the little creatures do their job. Perhaps OP means accelerated, as in the sugar present in the solution provides a rich growth medium for the yeast.