If it is a player's turn, and he moves one space, which results in pushing one or more other goblins, can he then make his second move, which may result in pushing yet more goblins?
Yes, "pushing" is like a normal move on a space with another goblin.
Imagine goblin "A" next to 4 goblins "B","C",D","E" in a square formation like this:
If a player moves his goblin "A" into goblin "B" who pushes goblin "C" who pushes goblin "D" who pushes goblin "E". Can goblin "E" push goblin "A"? This could go on infinitely!
Yes, they can stuck in a loop. This is a very bad thing when Rigor is coming.
But you know: goblins are very stupid!