My first question: let's say her base weapon is a +1 falchion. If she's a second-level kensai, can she give the weapon two levels of power (say, to make it a +2 ghost-touch falchion) or can she only improve it to a total of two levels? If she wants to make it a "+1, axiomatic" weapon, is that possible, or does she have to give at least it at least +1 of enhancement?
My second question: can a kensai change the powers in the weapon? For example, let's say a second-level kensai has given her chosen weapon (let's say a mace, perhaps) the powers of a +2 mace (Which would cost 160 experience points), and then gains a third level. I understand that she could give the weapon another (360 - 160 =) 200 experience points and make it a +3 mace, or a +2 shock mace, or whatever additional +1 bonus you please.
But what if she wanted to make it a +1 dragon-bane mace instead? Could she "re-empower" the thing, losing the +2 bonus, and readjusting the weapons' powers? If so, does she get to "reabsorb" any experience?
Are there any limitations to what powers she can grant her weapons? Can a sixth level Kensai really make her +1 falchion a +1, keen, vorpal falchion?
My a priori ruling: A Kensai should be able to re-assign the powers in her weapon. It takes the requisite amout of time, like any magic-item creation. If she's modifies the weapon when she rises in level, she only pays for any new powers (so, in the example, changing from a +2 weapon to a +1 dragon-bane weapon only costs 360 - 40 = 320 experience points); if she does so at any other point, all the weapon's powers are "flushed" and she would need to spend the full experience points.