What do you do with your brother who proposes frequently but never marries? And what is the expiation for your recitation of the Fatiha in front of him as a threat against him dissolving the engagement?

Merely reciting Al-Fatiha is not considered an oath that necessitates expiation. However, if it was accompanied by an oath and you intended to go with him and help him, then you may do so, and that is better if you see seriousness from him. In that case, expiation is required of you, due to the Prophet's (peace and blessings be upon him) saying: "Whoever swears an oath, then sees something else better than it, let him do that which is better and make expiation for his oath."