I'd like to exchange the Skills/Perks/Level Up part of the menu with one of my own design. Can this be done? Are there any tutorials on the subject?

What can and can't be done with the UI is a very blurry line. I'd say no for sure, but people have done amazing things. SkyUI, for example, changes damn near every part of the UI, none of which I thought would be possible.

However you may have a hard time finding someone who knows how to do that, that's willing to teach you.

if the menu prompt is a message item, and if the level-up distribution is handled by a quest through the Story Manager, then i would say yes. those would be editable

if it's a hard-coded game feature or baked UI, then SOL

Hmmm. Maybe I'll change all of the perks to match things in my game, and then grant points when they reach the "experience levels" I've designed.