My friend's nephew has warts all over his hands. I ate chips from the same bowl as him before I knew about it. Could I catch it on my hand from that?

Are warts infectious. "no." your risk of getting warts from touching the same bowl as him is extremely slight. The virus that causes common warts is everywhere. You have already been exposed. Some people are much more susceptible to outbreaks for reasons (relating to their immune system) that are not clear, while others are not. Your friend's nephew is susceptible, but has no more exposure than you.
Unlikely . Warts are viral infections and need to removed. They can be contagious but this sounds less likely to be spreadable.