Regarding the last question, if you have an encryption method that can encrypt 0 and 1 and has (efficient) algorithms for multiplying and adding the plaintexts

Regarding the last question, if you have an encryption method that can encrypt 0 and 1 and has (efficient) algorithms for multiplying and adding the plaintexts corresponding to encrypted messages then you can efficiently compute any boolean circuit. So any fast algorithm that can be computed without encryption can be computed efficiently by a homomorphic encryption scheme (in time that is some low degree polynomial of the time needed for the unencrypted algorithm).