Fist pump was Breakfast Club. Boombox was Say Anything. Lawnmower was Can't Buy Me Love. There was also a brief mention of Sixteen Candles. Hope this helps. :)
EDIT
also she mentions 'Ferris Bueller's Day Off' when she says that she wants her own musical number :)
gleaming the cube
easy
The 80s aesthetic is characterized by bold colors, neon lights, geometric shapes, and futuristic themes. Other key elements include big hair, shoulder pads, leg warmers, and vibrant patterns. Pop culture references, such as cassette tapes, arcade games, and iconic movies like "Back to the Future" and "Top Gun," also contribute to the overall 80s aesthetic.
Sixteen Candles, The Breakfast Club and Weird Science.
The Spoony Experiment - 2008 Spoony and Benzaie Discuss 80s Movies 3-10 was released on: USA: 18 May 2010
For example: References to Arsenio Hall and Jack Nicholson in Aladdin?
"The best selling 80s tee is the Transformer shirt. The Charlie Brown shirt is also extemely popular. Many 80s tees based upon movies are also good sellers, such as the Ghostbusters shirt."
easy
I am assuming it was to make him look more evil
'PG' had more leeway before 'PG-13' was adopted in 1984.
The second movie follows on from the first but 3 and 4 do not. They do contain references to the previous movies.
Plastic Movies Rewound The Story of the '80s Home Video Boom - 2014 The Future of Physical Media 1-6 was released on: USA: 2014