Will I have to pay a fee or royalties to the illustrator of my first book that I hired from a freelance service?
That should have been negotiated with your illustrator up front; typically you pay for all rights to their drawings. Usually they are allowed to claim credit for their illustrations and perhaps use them in their self-promotion, but not cannot re-sell them to anybody else, your contract with them signs over the copyright to you.
There are standard contracts for this; if you didn't get one or research this business agreement up front, your illustrator may still own the copyright on their drawings, you don't automatically get it if they weren't an employee of yours. (A contractor is not an employee).