How can I reconcile with someone who betrayed me and proposed to my sister, and he is acting arrogantly?

Your friend's involvement in what you mentioned does not justify abandoning him and severing ties completely, especially if he shows repentance. If he repents, then good; otherwise, abandon him if you believe it will benefit him. Otherwise, it is sufficient for you to merely offer greetings of peace to him, as offering greetings of peace severs abandonment according to the majority of scholars. However, if you fear harm from him to yourself or your sister, then it is permissible for you to abandon him and not offer greetings of peace, for sometimes a graceful abandonment is better than a harmful association.