Does a baby with a vsd have a higher chance of getting sick?

No. A vsd, or ventricular septal defect, is a hole in the wall that separates the ventricles of the heart. Vsd's typically close on their own as your baby grows. They do not predispose a child to increased illness.
Depends. If the vsd is large the patient is more prone to getting respiratory infections and should be immunized with antibodies against RSV until repaired.
Heart failure. A large vsd can cause congestive heart failure, failure to thrive, and make illnesses such as the flu or RSV very serious. Large vsds are usually surgically repaired in the first few months of life. Small vsds are not a problem generally.