I'm brand new to Sharepoint. How can I switch off web part's events like click and mouseover over title?
If your environment is customised at all (custom web parts, branding, etc), seek advice from your solution architect first, on the best way to do this.
If you wanted to remove the ability to right click throughout the entire page you can add a script to the MasterPage directly or better yet to a User Control loaded into the MasterPage that can supress the click events.
If it was only for specific web parts, then it would need to be built into that particular web part and you would capture the event on that container.