Mobility 6

Mobility 6 has a couple of effects:

1. You don't have to move in a straight line when charging

2. You can make your attack at any point in your movement

Essentially, it's like Mobility 3 with double the movement allowance, at the cost of provoking Attacks of Opportunity.

You get +2 to attack and -2 to Defense as normal for charging.

Mobility 9

Q: When you use Expanded Mastery 9 to make a tumble check when you provoke Attacks of Opportunity due to movement, does the result of your check set your Defense for the attack?

Not exactly. Your Defense doesn't change, but if your check beats your opponent's attack roll, then even if he hit your Defense, he misses.

For example, say you have Defense 27, Tumble +22, and Mobility 9. You provoke an Attack of Opportunity and your opponent hits Defense 28. He's hit you, but you can still use this ability to make him miss and to lose his ability to make further Attacks of Opportunity. If your check is 29 or better, he misses you (despite hitting your Defense) and cannot make Attacks of Opportunity for one round. If your check is 28 or lower, he hits you and can keep making Attacks of Opportunity.

Conversely, if your opponent had hit Defense 26, he would have missed you, but you could still have tried to make use of Mobility 9. If your check was 27 or better, he would miss you (which he had done anyway since he rolled less than your Defense) and he cannot make Attacks of Opportunity for one round. If your check was 26 or lower, he could keep making Attacks of Opportunity, though he would still not hit you (since your Defense of 27 beat his attack roll).

Q: Is this ability to make a tumble check usable every time that you provoke an Attack of Opportunity for movement?

Yes.

Mobility 10 vs Combat Reflexes 3

See Combat Reflexes.