I'm deep in Act 2, already moved my base to Santa Romera, sadly still flying the tug and.. I've got no missions to undertake.. none..

How to advance the game any further?

Hmm, you should have received a new ship about five or six missions into Act 2, well before moving to Santa Romero. Must have been difficult to get that far using only the tug! Been a while since I've played but I think you can change ships in the Loadout screen.

Note that there are at least a couple points in the game where you're apparently given no direction, no mission (IIRC Act 1 had one of these periods). Just fly around and do your thing, pirating, beating up Marauders, sight-seeing, whatever. After a few sorties you'll be contacted and the story advances. This might be one of those instances.

I think I had the same problem, the problem turned out to be that I didn't had garnered the support of all systems yet.
If this is the case visit all systems and run their errands and you should get new missions.

The game is broken. I already found pilots in all three systems and went everywhere. Last mission was with the Akila freighter which was destroyed. I still have no other missions..

I found the solution: uninstall the game, make a clean install and don't use any mods!
It's the mods spoiling it.