Do I need a special adapter?

For Bluetooth, no. For USB, you need a cable that matches your piano's USB socket and your iPhone's port.

Is there a delay between pressing a key and the app responding?

Bluetooth MIDI adds a very small delay. For reading practice and spotting wrong notes you won't notice it. USB is a touch faster.

Will the sound come from my phone or my piano?

From your piano. The app only reads which notes you play, so your piano keeps its own sound.

How to connect a digital piano to your iPhone (Bluetooth or USB)

A practice app can only tell you which notes you played if it can hear your keyboard. Most digital pianos do that over MIDI: not the sound, just which keys you pressed and how hard. Here's how to get that to your iPhone.

Option 1: Bluetooth MIDI

Plenty of newer digital pianos have Bluetooth MIDI built in, so there are no cables at all. Check yours.

Turn the piano on and switch its Bluetooth on (some models have a button, others a menu setting).
On your iPhone, open Settings, then Bluetooth, and pick your piano from the list.
Open the practice app. It should find the piano on its own.

If your piano doesn't show up, switch it off and on and try again.

Option 2: USB

If your piano has a USB port marked "to host" (usually a square USB-B socket), you can connect it with a cable.

Use a USB-B to USB-C cable if your iPhone has a USB-C port, or a USB-B to Lightning camera adapter for older iPhones.
Plug it in, turn the piano on, and open the app.

Modern keyboards usually work without extra drivers. The iPhone treats them as MIDI devices.

How to tell what your piano supports

Look at the back or side for a "USB to host" port, and check the manual or the maker's website for "Bluetooth MIDI". A piano with only a headphone jack and no USB port can't send MIDI.

What about acoustic pianos?

An acoustic piano doesn't send MIDI, so an app can't read which keys you press. Some apps listen through the microphone instead, which is less precise.