Fastest train Zurich/Cinque Terre ?

You might be having trouble finding schedules on the Bahn schedule website because you don't realize that Cinque Terre is a region, not a rail station. Use the town, eg Vernazza, where you want to go. I can find connections with only two changes, Milan and Monterosso. Or maybe you want to go to Monterosso, then one change and you're there.

Another possible difficulty is that the bahn.de website does not recognize the spelling "Zurich". If you type that in, the drop-down menu gives a bunch of choices, starting with "Zur Linde" in Aurich-Wallinghause, then "ZRH, Zurich airport", then a bunch more "Zur-something" options. None of the choices offered is "Zürich" unless you put in the umlaut to start. One can click elsewhere, to get rid of the drop-down menu to proceed (and to be able to enter a destination), and then it will go ahead with options for Zurich. But a newbie who thinks that drop-down menu offers the only choices can get stuck. The Swiss website, on the other hand, will take Zurich and turn it into Zürich HB without a fuss, but refuses to acknowledge that trains run from Milan to Monteroso or Vernazza. "No trains available" is what I get there (and for many other destinations within Italy.) It seems lite the Swiss are still mad about the Cisalpino divorce and won't recognize some small towns in Italy. These train websites, even Bahn.de, are not all that easy for first-timers. Each one has its own little quirks that you have to learn to deal with.

Actually, if you type "zurich hb" the bahn site will turn it into "Zürich HB". That's what I do. I just discovered that typing "zuerich" brings up the "HB" option (just like Zürich), also. Hm, 7 characters rather than 9. It also suggest "Zürich" and "Zürich Flughafen", but not "ZRH", which you get from "Zurich".