Can a monk fight with two weapons? Can she combine a two-weapon attack with a flurry of blows? What are her penalties on attack rolls?
A monk can fight with two weapons just like any other character, but she must accept the normal penalties on her attack rolls to do so. She can use an unarmed strike as an off-hand weapon. She can even combine two-weapon fighting with a flurry of blows to gain an extra attack with her off hand (but remember that she can use only unarmed strikes or special monk weapons as part of the flurry). The penalties for two-weapon fighting stack with the penalties for flurry of blows.
For example, at 6th level, the monk Ember can normally make one attack per round at a +4 bonus. When using flurry of blows, she can make two attacks (using unarmed strikes or any special monk weapons she golds), each at a +3 bonus. If she wants to make an extra attack with her offhand, she has to accept a -4 penalty on her primary hand and a -8 penalty on her off-hand attacks (assuming she wields a light weapon in her off hand).
If Ember has Two-Weapon Fighting, she has to accept only a -2 penalty on all attacks to make an extra attack with her offhand. Thus, when wielding a light weapon in her offhand during a flurry of blows, she can make a total of three attacks, each at a total bonus of +1. At least one of these attacks has to be with her off-hand weapon.
A 20th-level monk with Greater Two-Weapon Fighting can make eight attacks per round during a flurry of blows. Assuming she wields a light weapon in her off hand, her off-hand weapon attacks are at +13/+8/+3, and she has give attacks (at +13/+13/+13/+8/+3) with unarmed strikes or any weapons she carries in her primary hand. If the same monk also has Rapid Shot and throws at least on shurkien as part of her flurry of blows (since Rapid Shot can be used only with ranged attacks), she can throw one additional shuriken with her primary hand, but all of her attacks (even melee attacks) suffer a -2 penalty. Thus her full attack array looks like this: +11/+11/+11/+11/+6/+1 primary hand (two must be with shuriken) and +11/+6/+1 off hand.