Does the Investigator reply directly to a 483 or Warning Letter, or is it done through the sponsor since some of the observations might be the sponsor’s obligation?

Whoever the 483 or Warning Letter (WL) is issued to should be the person/organization that responds. In cases where a Principal Investigator receives a 483 or WL and there are some findings that require the sponsor’s input, the PI should work with the sponsor to obtain the necessary information but the response should be from the PI to the FDA.