Yes. I know that there are some protestants who pray the rosary regulary. I think another forum member, Zooey, prays the rosary, and she is a Methodist.
How would a nonCatholic benefit? Well, you are meditating on the life of Christ as you pray the rosary. I think that this will draw you closer to Him as you do this.
You are also asking His mother, Mary, to pray with you, too. Don’t we all need someone to pray with us?
Of course you can have a picture of her! Don’t you have pictures of family members, friends, etc? It’s not any different.