As far as I know, many gestures on the trackpad can be mapped to the mouse by placing the function on the mouse buttons. However, not all gestures can be mapped. On the other hand, there are functions via the buttons that are not available as gestures. Really ingenious are the functions that change depending on the software. There are buttons that have different functions in Photoshop than in Indesign or Illustrator. There are plugins and you can bend them to suit your needs.

For me, the MX Master is much better than the gestures. But that's not a general statement that applies to everyone.

Yes, they work and are already preset.
Customisable with the Options+ app from Logitech.
More detailed information can be found on the Logitech website.