In your first picture, the "spot" on the lower part of the new fan is something you want to watch out for for the next few days.
Make sure it is not spreading.
My initial thought was some kind of rot, but it could well be mechanical damage as you said.
By the way, this is very common way of paphs making more of itself.
Sometimes new fans will come out of in between leaves or by a way of "underground" shoots that pop up at a random place in the pot.
Sometimes more than one of them, making the plant bigger faster!
You can divide large paphs, but it's best to let them grow big because plants will give you nice flower show that way.
When you do divide, make sure you have at least 4 fans per division. You can make smaller divisions and plants will grow fine, but it may take longer to rebound and skip flowering for a seaon or two.
With bigger division, you have nothing to worry about.
Happy Growing!