Is there a direct train or not and if there is, where can I book this mysterious thing? http://www.trenitalia.com/tcom-en doesn't show anything despite this https://www.italiarail.com/airport-connections rather official looking page claims there's now a direct train from Florence to the MXP airport:
According to the trenit app (android, iOS), searching for trains from Malpensa to Firenze (all stations) and sorting by duration shows one change is required. I've tried several different days of the week and both Saturday and Sunday.
This 2010 newspaper article says there was a direct train:
DA Firenze, stazione di Santa Maria Novella, all’aeroporto di Malpensa sul treno super veloce, senza mai scendere e cambiare i.e. from FLorence Santa Maria Novella to Malpensa airport without having to change.
However, it was suspended after less than two years:
il precedente: il diretto da Santa Maria Novella a Malpensa è stato sospeso dopo meno di due anni
There used to be a direct high speed service in the past from Napoli Centrale, but the experimental line was ultimately abandoned after Expo 2015.
Today the only way to reach the airport by train is to change at one of Milan stations (for example Milano Centrale) connecting long distance trains with Malpensa Express service.
Passengers from Lombardia region and Switzerland can benefit from the other local train services operating in MXP airport station.