Can cleft lips and cleft palates be repaired?

Cleft repair. Yes, both cleft lip and cleft palate can be repaired. The website of the cleft palate foundation ( http://www.Cleftline.Org/ ) has useful information about cleft surgery and other aspect of cleft care.
Yes. Oral and maxilla-facial surgeons have been doing this for years with amazing results.
Yes. Yes, there is surgery for this. Usually, this is done during childhood. You would need to see an oral & maxillofacial surgeon (omfs) or plastic surgeon for this.