For the case of alpha decay, [...] the simple underlying mechanism is quantum mechanical tunneling through a potential barrier. You will find a simple explanation in any elementary quantum mechanics textbook; for example, Ohanion's Principles of Quantum Mechanics has a nice example of alpha decay on page 89. The fact that the process is probabilistic, and the exponential dependence on time, are straightforward consequences of quantum mechanics. (The time dependence is a case of "Fermi's golden rule" --- see, for example, page 292 of Ohanion.)
An individual does not necessarily have to be a musician to qualify as a member of the 27 Club. Rolling Stone included television actor Jonathan Brandis , who committed suicide in 2003, in a list of "members" of the 27 Club.  Anton Yelchin , who had played in a punk rock band but was primarily known as a film actor, was also described as a member of the club upon his death in 2016.  Likewise, Jean-Michel Basquiat has been included in 27 Club lists, despite the relative briefness of his music career and his prominence as a graffiti artist and painter.