I'd have to see your setup to give any more defense tips. As for getting out of the cave, looks like you've found a bug! I'll have to look into what could be happening there. Probably an event triggering out of order or not triggering at all for some reason.
That's fair.
Oh, I also found another issue while playing through the second area too.
I figured out a "workaround" of sorts to get resources without being bothered by the slimes, by only building in the higher sections so the slimes couldn't reach me.
As a result however, they just piled up on the ground floor beneath my buildings, and it rapidly caused my game to lag really heavily.