We don't know - the only snippet we see of Steve's life in the past is of him dancing with Peggy - but I firmly believe it's unlikely, for three reasons.
Firstly, Steve specifically chose to remain in the past with Peggy because he wanted to leave behind his role as Captain America, and just live a normal, ordinary life. In other words, Steve had retired from being Captain America. Rescuing Bucky, or preventing HYDRA's infiltration of SHIELD, would require throwing himself back into the lifestyle that he had deliberately left behind - and potentially putting Peggy in harm's way.
Secondly, as with most time-travel media, a recurring theme in Endgame is that meddling in the past can have unintended consequences, such as Loki's escape with the Tesseract in the alternate 2012. Steve has no way of knowing what might happen if he doesn't let 9/11 or the JFK assassination run their course; perhaps something ten times worse will happen later on down the line.
Thirdly, as we know from the end of the film, Steve always planned to return to the original timeline anyway. So there would have been no point in stopping any of those disasters, because when he eventually returned to the original, unaltered timeline, they would still have happened.