No difference. It is optional in both uses.
Student or Learner
I wonder about how Henry will get food and clothing.
According to a book, "about" here is not necessary.
"Try to make sense of what you see and wonder about what makes the universe exist.'
This sentence is from a quote of Steven Hawking. I am puzzled over why "about' is used here. Any difference on the two occasions?
Yes, to me there is a difference. "Wondering about what makes the universe exist" has the sense of "wondering about the universe" - being in a state of wonderment - which is not present in the first example. To me, 'about' is less needed in 1 than in 2.