Best to enter the customs zone with the phone powered off, your device's security is likely better in this state, less likely to be circumvented while you surrender it.
Things like mobile boarding passes and the "Mobile Passport" app encourage and train people to hand their devices over to TSA and CBP personnel. In that later case, unlocked and with an app CBP/DHS controls already installed (with a lengthy ToS no one ever reads).
1. There is no special app you need for mobile boarding passes. It has always been either a PDF or a PNG file emailed to you.
2. I was never asked to hand over my phone to TSA agents at any point. They just ask you to put your phone with the boarding pass QR code displayed over a QR scanner. At no point the phone leaves your hands.
As an aside, on iOS, the airline apps I have used work like the Wallet app and are visible on the lock-screen, the device must be powered on but remains locked when you display your boarding pass, etc.
Best to just wipe any device and restore from backup.