If demon magic is powered by fear, and Mao can temporarily get his powers back when surrounded by enough terrified humans, why doesn't he try getting some power by hanging around a movie theatre when they're showing scary movies?
Because he doesn't know about it. Even when he gains his power back during the Earthquake, he has no idea how and why it happens.
Pretty much this, and the manga adaptation specifically points out his ignorance of this fact. Emi even later muses to herself that, if Maou uses up what's left of his magic to kick-start a wave of terror, there's nothing she could likely do to stop him.
That, and it might be that the sort of fear people feel during these movies is not sufficient and it needs to be real terror. In which case he wouldn't be as eager to get it as he would've been in the past, seeing as now he started noticing that humans are actually living beings.
Confirmed in the 4th episode, Maou figured out the source of his power after the earthquake, but didn't want to make trouble for the people of this world.
Because, honestly, horror movies usually aren't terribly scary.
Have you even seen a Japanese horror film? Japan pioneering the survival horror game genre was not a simple coincidence.
How did Emi get her job anyway? Ente Isla seemed to be at middle ages in terms of innovation, yet she gets a job as a telemarketer which involves computers and tech knowledge?
The isle on which Satan's castle was appears to be like that. We haven't seen every one of the four islands, and we can also add the fact that Emilia, being a hero, might have had access to a bit more than normal people. That, and depending on the exact details some "telemarketer" jobs don't require prior knowledge but only ability to learn (which Emilia certainly had, since she was learning things and training for a significant part of her life). And outside of that it's Rule of Fun.
She's highly adaptive, smart and put in a lot of effort to learn? A heroic effort unto itself till she found and killed the Overlord at the time.
Small one, but in the first or second episode, Mao lists off a washer/dryer as a forgivable expense, saying that the coin washer down the street would add up over time. How does the math check out on that?
Why is Emi not trying to kill Lucifer constantly now that he's living with Maou and Ashiya, wasn't he the one that took over Emi's island and presumably killed her father? she seems a little too okay with him hanging around.
She may not be as much as a bloodknight as others are. Seeing value in someone's nature becoming impotent or redeeming themselves. If the person is no longer who they were, should she still be killing them? Though this doesn't really absolve Lucifer and Satan of the thousands of innocents slaughtered (s far as we know) like the young girl right at the start of the 1st episode, maybe spending the rest of their lives making up for this if they change is better than outright killing them and putting an end to whatever good they would have done. Maybe she just really LIKES our world and killing them would be disrupted, mixed in with the above and sincere doubts instilled in her since they aren't anything like she's been raised to believe (but most definitely have been like she taught till they came to this world, further confusing her).
We can see this in the chief inquisitors behavior as well, she's genuinely confused and aghast when Satan is showing a high level of sensitivity and empathy to Chi by citing her emotions, even bringing up her parents and their thoughts on their potential relationship. Most of the humans we've seen lack this emotional range and consideration.
Why was Suzuno so surprised at the 'man in a television set' if she had watched old Samurai flicks and shows as research for Japan? Wouldn't she have needed a television or theater for that?
Rule of Funny. We only learned about her watching them after we saw her freak out. Alternatively, she might have been playing that one, after seeing a character in some story react the same way and thus thinking that it was the appropriate response, as her behaviour in parts on Ente Isla show her as rather collected and thus unlikely to freak out in that way.
So wait.... if Maou, Lucifer, and Ashiya knew that Suzuno was from Ente Isla and that she had been poisoning their food why is Ashiya eating it if he knew it is what was making him sick?
Presumably, Ashiya didn't care, because either way, it was free food, and that meant it was saving money on other expenses.
That. And whenever he was apologizing about his "illness", he was apologizing for "being too weak". Combined with the fact that Maou and Urushihara ate the same food and were fine, there you go. Of course, in this case Maou was likely fine because he was stronger and Urushihara due to being a fallen angel and thus not hurt by this sort of poison, but the point stands.
The whole point of the scene where Lucifer smells the sacred power in the leftovers, but eats it anyways, was to show that they really don't give a damn as long as it's free.
Okay, but what about Chiho and Emilia? Why weren't they affected by the poison? After all, they did eat over at Maou's at least once while Suzuno was on her job, and since it is clear that Suzuno can poison humans, does this somehow mean that Chiho is stronger than Ashiya?
Because Sacred Power is only harmful to demons. Chiho is a ordinary human and Emi would probably get a tiny boost from eating it since she can harness sacred power.