This rickety wall is wobbling and is going to collapse.

Yes, it's fine. I'd actually use "and about to collapse", ie. the collapse is moments from happening. "Going to" is certainly not wrong, but the possible timeframe is much larger.

It looks fine to me.

Hey Hmano! Your sentence was correct as well, at least for Standard Wisconsinite English. :) In America it would be correct to drop the second, "is." But who knows? Maybe in England it's incorrect to drop the second, "is." It all depends on which country you are from and which area in a country you are from. :) Hope this has helped! Autumn