I thought "enter" is more appropriate regarding the smartphone, but is it better to use "punch" than "enter" here?
You're right, "punch" is an unusual word to use in this case. Better words to use instead would be "enter", "type", or "search". "Punch" still works in this case, although it is very informal and less common. To "punch something in" can mean to put something in, enter in or record something. However, this word is usually used in cases where you are physically pushing a button, as it implies more force. Ex: Punch in this combination on the lock to open it.