Fighting Monks aren't terrible in their attack strength in terms of defensive and offensive attacks, however they are only really let down by their complete lack of armour which makes them susceptible to ranged attacks. It also means that they get worn down very quickly in melee attacks as well, which means that you will need a very large group for them to be effective.
Fighting Monks move at a fast speed, and this makes them the ideal troops for quickly capturing an estate or moving away from enemy units, however any ranged units will easily decimate them. You must ensure that these units are protected by Archers or some other form of ranged unit at all times in order to successfully use them.
Fighting Monks can also be used well in conjunction with Warrior Monks, and to compliment them fighting. Though these units should never be used to take the brunt of the fighting, using them as secondary to Warrior Monks can be quite useful. Note that no AI lord uses the Monastery, and therefore, they do not use Warrior Monks. Please also be aware that no AI Lord in the game recruits these units.
You can recruit Fighting Monks from the rank of Knight Errant. You will need 25 gold as well as 1 Honour and 1 peasant from the campfire before you can recruit a Fighting Monk. Honour can be produced by the means shown in this article.