"People who watch things will have a tendency to do that thing."

Given the fact that millions upon millions of children play incredibly violent video games without feeling the urge to go on killing sprees, I'd say what you're saying is completely specious, but I can understand that critical thinking can be difficult.

In those video games people are in general playing as heroes. If million of kids where playing games where the "protagonist" was a school shooter then yes I believe we would see an increase in school shootings.

Do you also believe violent video games lead to more violence and should be banned?

You're trying to argue with a taboo.