1. Hello, how do I delete demos for whole collection? (so far I found only how to delete demos for each card seperately)
2. How do I remove iStripper from taskbar (when its closed and/or disabled), so that the software would stay system tray only?

You can Select Multiple cards at one time, then Right Click the trash can and Select Delete Previews only.

you can select your entire collection, although I recommend to do this is small batches...

on the My Collection Screen, Press Ctrl-A to Select ALL cards at one time.

The Minimize to the Taskbar Icon is by Design.
Totem wishes it to Always be visible on the TaskBar, when it is running.
But you can Right click the Icon, and close it..

You will have to do that, each time you minimize it.

3rd, There is a Safe for Work, Stealth Mode.
If you Select one of the Stealth Names and Icons...
then the X does Close the iStripper Window, and NOT display a Task bar Icon.

A Stealth Icon is still left in the System Tray area