It would be better to say: "There's only one employee/cook/cashier in this ramen shop. It's amazing. How can she handle all of this work by herself?" An "employee" is a general word for someone who works at a place. "Cook" is a person who makes food (I'm sure you know that), and "cashier" is a person who takes the money from customers to give them their food/items.
The first sentence is fine, but I agree with the above comment that "clerk" isn't really a good word to use for someone working in a ramenya.
For the rest of it: "That's amazing. How does she handle all the work by herself?" (This sentence expresses your surprise and wonder), or "It's amazing how she handles all the work by herself" (this sentence shows your amazement).