You can take a martial arts as a Quality, pay the karma and get one free technique.
Yes
The Martial Arts itself gains no +2, but the techniques you use do get a +2.
No. you get no bonuses or penalties of any kind for simply having a style. Having a style merely dictates which techniques you can have/buy.
At that point you can also take the Unarmed skill specialization of the Martial arts of the same name, thereby gaining the +2 to the martial arts and techniques.
You only get +2 when using a technique if you have a specialization in the appropriate active skill for a style that has that technique (and obviously you can't use a technique you haven't purchased). You do not get the +2 any other time
*. Note that if you have both "Karate" and "Jeet Kun Do" and you buy "Counterstrike" - then it count's as though you bought it for both (since there's no stacking bonus for Counterstrike). In that case you would get a +2 bonus to counterstrike rolls regardless of whether you had a specialization in "Karate" or "Jeet Kun Do".
You can never have more then a +2 in regards to any martial bonus or technique bonus for yourself or your foe(s). No stacking above 2.
Yes, but with a few odd exceptions. The yes part is: If we continue the example above and have both Karate and Jeet Kun Do, if you were to purchase "Yielding Strike (Counterstrike)" from Karate, you would not count as having it from both. You could therefore buy Yielding Force (Counterstrike) again from Jeet Kun do, giving you a total bonus of +2 when making a counterstrike. If you then bought/learned the Aikido style, learning Yielding force (Counterstrike) a 3rd time would give you no further bonuses. The exception is: There are a variety of different ways to get more than "+2" total, but this is done by stacking multiple techniques, styles, specializations, and qualities all together. I give an example at the end of this post.
So by their rules I can take a Martial Arts Quality but never had taken Unarmed Combat?
Yes. Note than not all martial arts style are designed to be used with unarmed, and some can be used with multiple skills depending on the situation, so this isn't exactly a completely odd situation.
Yes, if you wanted to take an action that used a skill you don't have, you would have to default on that skill. Having a martial arts style and no active skill to go with it follows the exact same rules. Especially since you never really "roll" your style. The style merely dictates which techniques you can have/buy.
You learn a formalized, in depth System, say Aikido, which takes a great deal of conditioning to do it right, and you have no unarmed combat skills, and only increase with a stat????
Yes, you could choose to have a style and no unarmed skill or no blades skill or whatever and always default on your rolls whenever you wanted to use a technique or make an attack that needed those skills, but I don't know why you would. You could also increase your skills later by simply spending karma to gain and increase the appropriate combat skill(s) as normal.
.....
Example: Say you have AGI 6, REACT 5, & Unarmed 6 with no specializations. You also have the "Jeet Kun Do" Style and chose "Counterstrike" as your 1 free technique. This is our base character. Let's name him Bob.
Bob would roll 12 dice when attacking with unarmed (AGI 6 + Unarmed 6).
When attacked by someone, Bob could use the counterstrike technique, and would roll 11 (REACT 5 + Unarmed 6) dice to do so.
Later, Bob decides to specialize in Unarmed: Jeet Kun Do.
Now Bob still rolls 12 dice to make an unarmed attack (AGI + Unarmed), but when using any techniques that are listed as "Jeet Kun Do" techniques, he gets +2 dice.
In this case he only knows "Counterstrike" and so would be rolling 13 (5 REACT + 6 Unarmed + 2 for specialization) dice to make counterstrike rolls.
If he later bought another Jeet Kun Do technique, he would get +2 dice when using it as well, assuming the technique requires a roll of some sort.
Later Bob learns "Yielding Force (Counterstrike)".
Now Bob still only rolls 12 dice for a regular attack (AGI 6 + Unarmed 6), but when making a counterstrike roll he rolls 14 dice (5 REACT + 6 Unarmed + 1 Yielding Force + 2 specialization).
Specializations can be really good (as usual), or a waste - depending on what all tech's you have or plan to get. For something like "Kick", "Randori", or "Bending the Reed" a specialization would give no benefit. Whereas for something like "Called Shot (Disarm)", a specialization would net you +2 dice on the disarm roll, but it's cumulative with the -4 for making a called shot, so you would end up with only a -2.
.....
Stacking bonuses and penalties example: Some other techniques and qualities can be combined though, so if you had the "Sharpshooter" quality, Knight Errant Tactical Style, a specialization in "Unarmed: Knight Errant Tactical", and had purchased both "Called Shot (Break Weapon)" & "Broken Fang" techniques, then when you made a called shot to break weapon you would roll your base dice -4 for a called shot, but then reduced to -2 (due to Sharpshooter), further reduced to only -1 (due to broken fang) and then increased by 2 more dice (specialization) for a total dice pool of base +1 (a total of a 5 point effective difference from baseline).
*:Although, like I said earlier, this is up for a little debate. (Some people like to give the +2 whenever the GM/player agree that it would make sense to be able to fully utilize the martial art in question. The problem here is that not everyone can always agree on when is appropriate due to varying degrees of people's real life knowledge about various martial arts styles.)