Do I still have to go through customs if I have Mobile Passport?

Yes, you still need to go through customs even if you have Mobile Passport. The app lets you send your info a little bit ahead of time to speed up the process, but you will still have to present your official passport and briefly talk to an agent. Also, your bags may be checked at random, regardless of whether or not you have the app. You will be able to use a designated Mobile Passport line that should let you bypass the majority of the crowd.