• "Oldschool": No fancy 3D graphics, no realtime playing - just turn based, tile map.
  
• Should be cross-platform - I think the best way is to use Java - any other recommendations?
  
• I already made a few simple games - some "shoot' em up", Pong, that stuff; fiddled with bitmaps in Delphi way back on Windows.
  
• I'm not sure on whether to use a pre-made engine. While it would speed things up, I'd rather know what goes on "behind the stage", and I don't know if I can achieve that without creating from scratch. Any advice? (Oh, and if I were to use something pre-made, it'd have to be licensed under some form of copyleft so I don't have to struggle with licensing problems.)
  
• As mentioned, I made some simpler games with Delphi's VCL. But I really don't know where to begin with this one, and albeit having searched the internet for a long time, I didn't find any tutorials that really addressed my problem. My hope now is that the community in this forum can point me a way to start.
  

You could also consider an open-source engine as a compromise solution: this may speed things up and you can learn things "behind the stage" as you will become more expert.

Typically there are compilers/interpreters for major languages on major platforms, so you could also consider other languages.

I'm not much of a Java programmer, but I've heard good things about jMonkey.

Have you considered something like ActionScript? Artists in my university use it to make simple games that turn out to be pretty good too.