Ok, I am a new member and I have joined to get feedback on this question I am stuck on.
Welcome to the board.
Radiant inner peace is dependent on the realisation that my inner being is immortal. How is this a certainty? Isn't this a belief based on faith?
There is some faith involved in Buddhism. Mahayana Buddhism says that when we eliminate all our illusions we are able to see our true self. Our true self is said to be eternal and unchanging. Only a Buddha can clearly see this and we deluded sentient beings don't understand ultimately what this means. Because I don't know what it means, I leave it's meaning an open question in my mind. I have some idea what it means but am definitely not certain. But I do accept it, whatever it means, as a matter of faith. Why do I have faith? Because I have developed trust in Buddhism.
I thought that Buddhism is not a religion and does not require any faith?
I think that Buddhism is both a religion and a philosophy. There is an important distinction between blind faith and faith that comes from trust. With blind faith one is blindly believing anything but faith that comes from trust is different. For example, if a boy has parents who don't care about him and lie to him all the time trust in his parents would be misplaced. But suppose a boy has parents who deeply cares about
him and is honest with him, it is reasonable for him to trust them.
How do I know this concept of 'rebirth' is true?
I'm not sure about what rebirth in Buddhism means, but for sure in Buddhism the self is not what ordinary people consider it to be. Ordinary people consider the self to be the physical body and/or something that they call the soul which they say inhabits the physical body. In Buddhism the self is much different.