Yes. All surgeries have risks associated. Ptosis repair complications can include: inability to close the lid fully (potentially leading to corneal drying/damage), asymmetry between appearance of lids on the 2 sides, scarring/thickening of the lid, in turning or out turning of the lid (& therefore the eyelashes) and of course residual ptosis.
Minimal. For adults, ptosis surgery involves anesthetizing the lid, opening it and finding the muscle that lifts the eye (the levator) and shortening it to elevate the lid. There are variants of this with slightly different techniques sometimes dependent on the cause of the ptosis. Risks are largely positional: the lid may end up too high or too low and it may not match the other eye.