It certainly can and does. A commercial can imply that something is popular, or that doctors are recommending it. Polling companies along with 'news' pundits can shape expectations and manipulate fence-sitters with fear of having their vote 'wasted.' A popular message in culture can be internalized by a segment, or even a generation (You Gotta Fight For Your Right to Party, We're Not Gonna Take It, With Great Power Comes Great Responsibility, May the Force Be With You). CIA and others would, and probably have, used media arms in foreign countries (and probably domestically) to normalize what they wish, and desensitize what fits agenda.

The older I get, the more of media appears to be soft disclosure, or allegory to what the author cannot or is not willing to talk about, but I don't think it's much of it. For instance, there are TV shows and movies where corruption between federal departments and law enforcement and organized crime and globalist organizations and NGO's are depicted by people who have experience on the matter or have consultants who do. There are fictional accounts of 'possibilities' that in some capacity become more true as time passes. Not exactly, as it is always exaggerated (Demolition Man, RoboCop, Eagle Eye). There are soft disclosures or cases where media is used to make more well known the way things work behind the scenes, the 'kinds' of things that are happening, or little known situations that have already happened. I wouldn't bet these are examples of that, but it would look like this: Blacklist, Person of Interest, NCIS, Law & Order, Burn Notice. Those who believe in predictive programming overestimate the extent to which the 'programming' part is preconceived and premeditated by the author and producer. Most often I think we see people who have their finger on the pulse of the way society is headed, and an understanding of first principles and the nature of cause and effect which allows them to 'see the future,' i.e. predict where things are likely to go, or are in danger of going. Occasionally these people also have clearances and want to make a bunch of money in Hollywood and/or disclose what they can to the public, and even more occasionally they have a mandate to do so by some group or agency. In the latter case, it is cheesy and forced just as often as subtle and subliminal and ominously injected.

Predicts. Rarely would the 'flying car' in a story be the first time it is thought of. However, I am sure that AI will troll fiction to find different ideas on ways of achieving things. As an extreme example, 'find all the ways to commit a murder without being caught' using all the detective movies and serial killer thrillers to help a criminal. As for more specifically technologies, sometimes fiction is used to portray technologies that are not yet public. But a creative person can imagine what must be possible in DARPA labs without having clearance there.

I can't think of a particular example that's better than Idiocracy. I'm sure someone better read could find something much better from the past.

'Programming' in most contexts is going to imply 'without the subject's awareness,' and certainly where government is involved it will tend that direction. Where 'predictive programming' implies manipulation, it is always immoral and, because the universe has a fabric worth living for, (conversely nihilism is non-functional), it is also not optimal for achieving ends. But it is certainly possible that creating fiction that is known and understood to be 'a look into a potential future,' or similar, could be useful.