Attacks with Q-Staff (no Flurry), +4 to hit, 1d6+6 damage.
Assuming you're using it two-handed, yes.
BAB+0, Str+4 = +4 to hit, and 1.5x strength to damage for using two hands.
Flurry of Blows with Q-staff: +3 to hit/+3 to hit, 1d6+6, 1d6+6 damage.
Flurry of Blows (Ex): "A monk applies his full Strength bonus to his damage rolls for all successful attacks made with flurry of blows, whether the attacks are made with an off-hand or with a weapon wielded in both hands."
So your flurry will be +3/+3 (1d6+4)
Then at Level 2, does it change to +4/+4 while flurrying, 1d6+6/1d6+6?
Way of the Weapon Master (Ex): "At 2nd level, a weapon adept gains Weapon Focus as a bonus feat with one of his monk weapons."
Assuming your quarterstaff is your selected weapon, it's:
Flurry +5/+5 (1d6+4)
BAB+2, Str+4, Flurry-2, WeaponFocus+1 = +5 to hit
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It depends on exactly when the monk wants to use his Crane Style. If he wants to use it during his turn (say, to deflect an AoO that he provoked somehow) then he has to keep his hand free at that moment.
So if he used his quarterstaff two-handed to attempt a trip maneuver (without having greater trip) then his hand isn't free and he can't deflect the AoO he provoked. But nothing stops him from freeing a hand after his attack is over in order to have it free when it's NOT his turn. This would prevent him from using his quarterstaff two-handed to take any AoOs that others might provoke from him.
While the quarterstaff is a two-handed weapon, there's a feat that lets you wield a quarterstaff one-handed, if that's what you want to do in order to keep a hand free. (Edit: the feat is Quarterstaff Master from Ultimate Magic
So, when you are able to swing just once, you get the 1.5 strength modifier bonus because there isn't any reason why you wouldn't use it to its max effectiveness damage wise.
It's not about swinging once, it's about not using Flurry. Flurry causes all hits to be 1x strength.
If your (non-flurry) BAB was +6, and you used a full-attack to attack twice, each of those would be 1.5x strength if you were still using it two-handed.
Say this Monk wants to use Crane Style to better defend himself.
1. Possible only when swinging once for 1d6+4
2. Possible only when flurrying
3. Never possible because you aren't fighting unarmed, or never have at least one hand free
Crane Style (Combat, Style): "You take only a –2 penalty on attack rolls for fighting defensively. While using this style and fighting defensively or using the total defense action, you gain an additional +1 dodge bonus to your Armor Class."
You don't have to be fighting unarmed or have a hand free.
It only applies when fighting defensively or taking the total defense action.
Total Defense is a standard action, so it's not really applicable to your question.
Fighting Defensively as a Full-Round Action: "You can choose to fight defensively when taking a full-attack action. If you do so, you take a –4 penalty on all attacks in a round to gain a +2 dodge bonus to AC for until the start your next turn."
Flurry of Blows (Ex): "Starting at 1st level, a monk can make a flurry of blows as a full-attack action."
Flurry is still a full-attack action, so you can combine it with fighting defensively. (Yes, it's a weird full-attack action with lots of other restrictions, but it still works)
Note that you can also Fight Defensively as a Standard Action so if you want to hit and move, you can still do so.
Monk: How does a monk's improved BAB when flurrying interact with feats like Power Attack and Combat Expertise, which have different effects depending on your BAB?
The monk uses his improved flurrying BAB to determine the effect of those feats.
—Sean K Reynolds, 07/08/11
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OK, so I started using the Quarterstaff with flurry of blows at 1st level Monk (18st, 17dx). You guys say that would be two attacks +3/+3 with 1d6+6. Using PCGen program it gives me a -2/-2 with the Quarterstaff. I'm assuming that is wrong. But now I'm drooling over the Dire Flail for 3rd level Exotic Weapon Feat. If I take the feat for using it, does it become a Monk weapon then? PCGen still gives me minuses with it for both attacks.
On the other hand, if the Monk only gets 1x his ST bonus for Flurry instead of 1.5x with a two handed weapon, there is absolutely no point in ever using a two handed Flurry weapon. That restriction absolutely neuters flurry and two handed weapons.
When using Flurry Monks treat their class level as their BAB, so an 18 Str Monk performing a Flurry would be +1 (Bab) +4 (Str) -2(Flurry) for each attack, so total Attack Modifier is +3/+3.
Now you do have a mistake/typo in your damage. Since you only use your base strength mod during a flurry (no 1.5x for 2h or .5x for off hand) you're dealing 1d6+4, not 1d6+6.
Being Proficient with the weapon will not turn it into a Monk weapon, so no flurrying at all with a Dire Flail.
That is why the only time a monk normally bothers with 2 handed weapons is as a Sohei monk, or an unchained monk. The Sohei can treat entire fighter weapon groups as monk weapons, and the unchained monk does not have the restrictive flurry of blows to only deal normal strength damage.
But now I'm drooling over the Dire Flail for 3rd level Exotic Weapon Feat. If I take the feat for using it, does it become a Monk weapon then?
I assume you mean the Exotic Weapon Proficiency (Dire Flail) feat.
Taking that feat does not mean that a Dire Flail becomes a "monk" weapon for you, it just removes the non-proficiency penalty.
There are some feats that make a weapon "flurryable".
Crusader's Flurry (for those with channel energy and the deity's favored weapon)
Feral Combat Training (for natural weapons)
Eberon (legacy DnD) had a feat (Whirling Steel Strike) that allowed flurry with a longsword. Most Pathfinder monks just use a temple sword instead.
Anything else ?