Damage

Oh, Infodude, that is because when you had other weapons on your damage was strength based. However, after equipping knuckles, damage is will based. Str effects damage with knuckles very little. As such, it's better to wear a title like Connector of Connous and Rano.

More like str doesn't affect damage with knuckles at all.

There is still a possibility that str effects things such as Knuckle Balance, I believe. But that's just a theory right now.

It doesn't. I used Tybalt's Fencing skills and saw no change at all in my stats.