If I want to pay someone back, do I need to stay close to the person I am paying until the transaction is fully completed?

No. The payer's and receiver's devices only need to be held close to each other while scanning the QR code.

You can also pay back the recipient remotely using the 'Contacts' button at the bottom of the main screen. However, for this to work, the recipient must have the Payconiq by Bancontact app and a bank account linked to the app.