I'm a big fan of the genre, but like many others I couldn't get over several issues with Dwarf Fortress. Rimworld doesn't quite do it for me either, so I have high hopes for you guys. :) 

One thing that I consider very valuable however is Z-levels. Will I be able to actually dig into the mountain and go too deep and too greedily?

There was a discussion on the pros and cons of Z-levels at https://www.kickstarter.com/projects/rocketjumptechnology/king-under-the-mountai... and a conclusion at https://www.kickstarter.com/projects/rocketjumptechnology/king-under-the-mountai...

In short, sadly no, though there'll still be mechanics about digging too greedily and too deep!