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Farms are supposed to give you 4VP plus one per troop and one per knight. Is that correct? If I have three knights and four mustered troops, that should be 11 points?

Similarly, with the castle, if I have three saracens, one prussian, and one serbian, then the castle bonus should be five points, correct? (Four points, plus one more for having a single set of three different enemies.)

Or have I misunderstood the rule?

Yes, I think you are misunderstanding the bonus for the IV level buildings.

Level IV Castle =
Earn 4 Influence for each set of 3 different enemy tokens (Saracen, Prussian, and Slav) in your play area.

So you get 4 points per full set, not 4 points +1 for each set.

Similarly the Farms give a bonus of 1 point for every knight and every troop. So no extra 4 points.

You get one point per level of the building you are building. You get these points immediately and is attributed to the building action.