For some people, whenever they enter a secret area, like the cave with thrown bladed weapons some time after getting wolf form, the secret count remains zero. I was thinking to buy this game, because Steam unfortunately hasn't brought it yet, so i have to inquire about.

And how the hell bat form travel works, once you reach an obelisk with the relative commentary?

Can't speak for the vanilla GOG version (I use Verok's patch, which is highly recommended), but the secret count works for me.

As for the bat travel, you need to enter the Bat Form in an outdoor area, highlight the needed landmark (A/D or Left/Right) or Bat Beacon (W/S or Up/Down) and press F6. It's a bit more intuitive with the gamepad controls.

There are exactly 0 problems with the secret's counter in the original vanilla version (I am about original kain.exe).
I did not see yet kain.exe of gog, but I know that sometimes they can corrupt the main exe and introduce new bags.
Verok's mod does not change this (almost all) moment(s) of this game.