What are the risks and the recovery time of balloon sinuplasty?

Low and short. When done for the right reasons for chronic sinusitis, sinus surgery (balloon or otherwise) is 90-95% effective at reducing symptoms. Recovery time is shorter (1-3 days) with balloon sinuplasty, and I do this procedure in-office with local anesthesia. Risks are low but similar to any sinus procedure: scarring, bleeding, infection, recurrent disease, eye/brain injury, need for further surgery, etc.
Recovery time varies. Recover time will vary depending on many factors including age, general health of the patient, infection control, smoker or not, blood sugar control, the exact type of procedure, and post-operative and follow up care. Discuss it with your surgeon and get their opinion as to what they feel is a reasonable recovery time for you.
Recovery varies, but. Sinus surgery leaves much to be desired for many patients. Sinus surgery for chronic sinusitis is often performed multiple times & is rarely deemed to be curative. In sinus surgery, scar tissue may form; recurrence & persistence of inflammatory or infectious conditions in the nose & sinuses, & untreated systemic illness all doom many sinus patients to failure and recurrent operation.
Arrhythmias Ischemia. The risks of angioplasty include arrhythmia (irregular heart rhythm) ischemia (reduction in blood flow thru the artery) injury to the artery being treated. Most procedures are uncomplicated and discharge from the hospital in a couple of days. Prior to the procedure ask and discuss the risks and possible alternative therapies with your cardiologist.