Well your in luck as both a browser and email client are currently in active development.

Just take a look at;

https://wayfarer.icu/ & https://iris-morphos.com/

Word of warning though, on a MacMini you might struggle to use the web based applications you have listed.

Wayfarer is a brilliant modern browser, based on up to date WebKit and it can virtually load any modern website, the issue is that a MacMini G4 is from 2004 and therefore limited in processing power. Wayfarer is great at news websites, YouTube, even most national TV catchup/on-demand services, facebook is even useable but where the hardware struggles is with power intensive webapps.