I am using the Private Sale Service on www.luxuryphones.net and have now found a buyer; are you involved with the payment?

No the payment would take place directly between you and the buyer.

Would you have some recommendations about the payment if the person who wants to buy my phone is located in another country?

If you are being paid by bank transfer we would suggest that - after you have received the money - you check with your bank where the money came from (bank, name of account, etc.). If it is coming from a different person than expected you could always tell your bank to return the money to the sender.