A new paper determines that yes, American media has indeed been covering Donald Trump disproportionately—and favorably.
The Harvard paper is arguably Old Media-skewing in its methodology. It assesses that pre-primaries period via stories by eight organizations: CBS, Fox, the Los Angeles Times, NBC, The New York Times, USA Today, The Wall Street Journal and The Washington Post. [...]
Its data concludes that Trump coverage was "favorable in all of the news outlets we studied. There were differences from one outlet to the next but the range was relatively small, from a low of 63 percent positive or neutral in The New York Times to a high of 74 percent positive or neutral in USA Today. Across all the outlets, Trump’s coverage was roughly two-to-one favorable."
USA Today edged out Fox News for most favorable Trump coverage, but all outlets dedicated more time to positive or neutral stories about Trump than negative stories. Which is puzzling because golly, it sure seems like there might be a few negative things to report about Donald Trump.
On the other hand, Hillary Clinton was the subject of more negative coverage than positive. So yes, both of the things you suspected were true have been measurably determined to be true.
The paper estimates the value of Trump's positive coverage at around $55 million. That’s what it would have cost the Trump campaign to buy pro-Trump advertising of the scope that the eight media institutions provided for free.