thanks for looking!

It's great to get this feedback. It truly leads to improvements...

I was thinking on leaving the 90 degrees thing as is, but I gave a second look and found an easy way to make the player turn around the corner. So, the more details I can take care of, the better!

Maybe I can also detect the end of a holding ledge, so the player won't fall when strafing - just stop strafing, and decide if wants to fall or to strafe the other way.

I don't understand very well the thing number TWO. You are talking about a narrow ledge, right?
the player can hold with his hands on narrow ledges, but can't climb on them because there is no room. Inversely, he can't walk on them because he'll fall. I think this is right. Althought these situations (when a ledge narrows) should be avoided in the game design.