If so, how much would a surgery like that cost?
There are many surgeons that will regularly perform this repair if needed during a cosmetic rhinoplasty. Sometimes all that is involved for internal valve collapse is rotating cartilage in the area and placing some sutures. Other times grafts may be needed to widen the valve area. If it is an external valve collapse then supporting grafts along the nostril can be used to support the rim. Consult a physician who regularly performs rhinoplasty surgery who can discuss the details further with you in person.
Yes we commonly fix both functional and aesthetic nasal issues at the same time. Sometimes however opening the nasal valve may make the nose appear wider which may not be part of the aesthetic goals. It's important to discuss these issues with an experienced rhinoplasty surgeon. Cost is variable in Toronto may vary from $5000-$14000 for rhinoplasty.