My entirely fanon, non-canon ideas are this:
1. Vault 111 had its population killed by the Institute because it was resource strapped and they needed the nuclear reactor energy of Vault 111 in order to provide them power for their experiments and expansion. They only left enough power for Vault 111 to maintain the Sole Survivor and his wife who were to be kept on ice until problems were resolved.
2. They replace people about the Commonwealth out of paranoia and fear for their lives. The Institute really does think the Commonwealth is a huge danger to them and a bunch of savages who are always plotting against them. They thus send Synths to constantly monitor and keep them under surveilance as well as sabotage any anti-Institute efforts against them.
3. The release of the Super Mutants on the Commonwealth by the previous Director is to keep the Commonwealth divided and weak so they don't have to fear any retaliation. The Institute is very paranoid about being murdered by surface-dwellers.
4. Father kept the FEV experiments going because he was hoping to be able to cure his cancer with them. He was actually considering turning his father/mother over to Virgil in order to see if that would help him with it. When Virgil departed, Father gave up on it and decided to reconnect with his parent and Synth child instead.
Note 4# is monstrously selfish and evil but backed up by the terminals.