Beyond the Flesh actually describes what's going on here, but it's not immediately obvious that it would.
A physical melee weapon will act as a semi independant entity, attacking foes nearby each turn while also replacing Strength and Dexterity with 60% of your Willpower and Cunning, for accuracy and damage calculations. This stat usage modification will also apply to conventionally wielded weapons.
Note also that leveling Resonant Focus from the Finer Energy Manipulations tree will increase that 60% to eventually slightly more than 100%. So assuming everything is working is as advertised (and I don't think there are any outstanding bugs for BtF):
1. Is the accuracy of your mainhand weapon now determined by Cun like a TK weapon or does it still use Dex?
2. Do these attacks benefit from Combat Accuracy and Weapon Mastery or am I just wasting my points?
3. Do these attacks use Physical Power and crit for damage calculations?
1. Yes, by default both your mainhand and TK weapons will use 60% of your Cun in place of Dex in calculating accuracy. I'm not sure how this interacts with Mindstars, since they're weird with stats.
2. They should! Stat substitutions don't change the fact that these are otherwise standard weapon attack. If you aren't leveling Cun much, or if the 60% penalty is making you miss a lot, this would definitely be a good time to level Combat Accuracy. Some builds will want to hold off on Weapon Mastery if they're trying to get Exotic Mastery, but most of the time you won't need to worry about that. If you're going for Mindstar Mastery, same deal. That's more of a concern, since MS is often strapped for generics.
3. Yes. Again, generally everything that looks like an attack, is an attack, in ToME. It would actually be a really interesting (and probably pretty broken) effect to swap physical/mental/magical power/crit/speed. ...sort of seems like something a Sollipsist should do, but that's beside the point. If an effect describes itself as a spell or mindpower [edit: or wild gift
and does not reference making an attack], those are generally the times when it will implicitly use spell/mind stats.
EDIT: see next post. I made a dumb.