I've been curious for a long time now on wen we as a people began being interested and even obsessed with other peoples lives; specifically people who star in movies or are on the cover of a magazine.
Hello - interesting question!
English newspaper historian here. I'd argue that, in England at least, we can perceive an answer to your first question from as early as the first of the periodicals emerging in the years following the restoration of the monarchy (from 1665, specifically, with the Oxford Gazette - it would become the London Gazette a year later when the court moved back into the capital.)
Before I continue though - there's an argument to be made that it occurred sooner than that. Corantos (literal translations of Dutch news sheets) had appeared relatively frequently as early as the 1620s, with newsbooks following shortly after. They contained international news almost exclusively, but certain influential figures - such as the Prince of Orange - would often feature to no small extent.
Moving back to the post-1660s: the London Gazette was the archetype of print news for a long time. Domestic news was essentially banned with licensing in place, but when regulation lapsed in 1679 (and again from 1695), a number of domestically-focussed regular newspapers emerged. This, I think, is where we can see a sustained interest in 'newsworthy' people really begin.
I'll use Titus Oates as an example. Just before 1679, Oates 'discovered', or invented, a Catholic conspiracy to kill the king, which became known as 'the Popish Plot'. Though the Gazette largely avoided reporting on it (aside through the governmental proclamations it was forced to publish), Oates still came up every now and then, and he was a major figure that appeared in the papers during the following year. The new periodicals brought him into the limelight so to speak, alongside all manner of news pamphlets discussing his testimonies and evidence. With the reading public extremely eager for news of any type, figures like Oates became something of a novelty.
There are a fair few other examples from this time period too. If anyone's interested in reading more, John Sommerville's The News Revolution in England offers an interesting way in for the beginner.
The term "Lisztomania" was coined to describe the hysterical behavior of Franz Liszt fans in the 1840's. The primary source accounts quoted in the Wiki article support arguments of a "rock star" characterization that was unprecedented to contemporary observers.