Is it permissible, when reciting according to Khalaf, to substitute the hamza if it is in the middle of a word, such as "بِرَأْسِي" becoming "بِرَاسِي" and "جِئْتُ" becoming "جِتُّ"?

If you mean reading behind Hamzah, then Hamzah replaces the hamzah in the middle or at the end of a word when pausing, but not when continuing. This applies whether the hamzah's sukoon is original or acquired. Hamzah replaces the hamzah with a long vowel (harf madd) of the same type as the vowel preceding it: an alif after a fatḥah, a yā’ after a kasrah, and a wāw after a ḍammah.