Does pressing the Force touch trackpad hard damage it?
The force trackpad is a piece of glass that doesn't move, but provides feedback based on where your fingers are using motors. Cleaning it with the damp cloth probably confused it as to where your fingers were, providing strange feedback until it dried a little.

But yes, really pushing your trackpad really hard could hurt it just like pushing on a piece of glass really hard can break it, but that seems unlikely given the strength of the glass.

As a fun experiment, shutdown your mac while clicking on the trackpad. You can tell when it shuts down completely because the trackpad stops clicking.