Ore ga Akuma de, Aitsu ga Yome de

I think you are partly correct. More like when Uika is about to die, Anzam will sacrifice himself/save Uika. Of course, we will find out why Anzam was thrown out of Heaven. However, he will redeem himself through this selfless act. As a result, he will become human and they can finally be together (most likely a time skip). It wouldn't make sense for Uika to die partly for three reasons

1. The idiot trio has said that Anzam does not kill people and will not let them die. There is no reason to think this will change when he will clearly love her later on
2. It would make the priest incredibly sad
3. There is no tragedy tag. In addition, this is a cute, light-hearted manga, so I doubt she will die.

A better question is why Anzam was thrown out of Heaven because he really is a nice guy (aside from the times he is mean/crude to Uika). Possibly he saved someone (a love interest maybe)? Not sure what the rules of Heaven and angels in regards to humans are ...

1. Eating like a westerns is a must

That we'll get a reveal to the reason for why Anzam got boot out of Heaven near the end.
Then once Uika die, she get to go to heaven, but in that moment Anzam will redeem himself from whatever sin he committed, and get to go to heaven with her.

And then they get married, again, in heaven.

of course all priests take shotguns with them while out shopping, it goes this the job xD