I'd like to get rid of tutorial popups and be able to omit cutscenes on a second playthrough.

For the cutscenes I have already found out that you just have to uncomment a line in "keybinds.ini". Then you are able to end cutscenes by hitting ENTER.

Is there a way to also disable the popups, or at least allow me to click them away at once and not only after a wait?

It would be wonderful if you could elaborate on that uncommentation further instead of just hinting towards it, so others could benefit from this aswell.

Well, if you think this is necessary.
Go to your Venetica directory (the directory where the game is installed, not /user/data/... or something) and open keybindings.ini with any texteditor. Somewhere close to the top you find these lines:

// cancel running cutscenes
// KC_RETURN = CutsceneMgr:cancelCutscene()

remove the // from the lower line (uncomment it), save and you're done. Now you can press ENTER to cancel cutscenes.