1: Admittedly I know little of Battlestar, but Zeno does have access to a ship with FTL and can speak. So...Hopefully he's got this in the bag?
2: Zeno can completely and utterly obliterate anything short of literal magic, even the trolls wouldn't be much of a problem as depicted in the film. As long as Frodo can get his ass to the volcano, Zeno's got this EASY. A very significant chance Zeno tries beating up Sauron if only to get his helmet because it looks cool.
3: Judgement day was inevitable. X_X He can't stop it. Even if he kills off every single person even THINKING of making a super AI in the universe some random dude will build one out of a microwave and blender and the cycle continues.
4: Well as the creatures canonically are strong enough to handle an exploding planet and countless years of space exposure, he's going to have issues with this. If he gets his ship he can just throw the asteroid into the sun.
5: No way in hell the Creeper can seriously harm Zeno, but on the flipside the Creeper is pretty horrifying and seems destined to always revive. Zeno might be able to just eat the thing? Can it survive being torn apart from the atomic level?
6: Seeing as Sinbad figured it out himself, Zeno can only help in this regard.
7: Oooooh yeah Zeno's not going to be able to handle the Kraken. Outside of orbital strikes with starship, Zeno loses this one hard.