Crowley always thought to himself that he didn't "Fall", especially not with a capital F, but Sauntered Vaguely Downwards. Hung out with the wrong crowd. Asked too many of the wrong questions. Or possibly just asked questions in general; not very angelic to question anything. And it was certainly not something he had stopped doing because he was a demon. He was pretty sure that those questions had gotten him assigned topside. You ask someone one too many times why a cute chameleon represents their true self and end up on Earth for the next 5000 years.
Not that that stopped the questions. He asked them to Aziraphale every time they met. And while he often got the Angel Party line in verbal response, he was fascinated by how very much Aziraphale didn't agree with the things he said. Other angels, and demons for that matter, were 100% firm in their convictions on, well, everything. Aziraphale didn't do more than pause for a second when all the children in Noah's vicinity took an unexpected journey (some would say in the blink of an eye) to some very tall mountains to the southeast of them. In fact, he stopped by, during and after the Flood to counteract Crowley's "evil" influence on the children. Crowley's not sure if either side would be happy with the fiercely independent, always questioning, yet also very faithful in their beliefs people they raised*. Both of them mutually agree to leave it out of their reports.
*Millennia later, despite them not having anything to do with it, Adam is largely the same.
Crowley also continues to question God. He's not sure when he started up again after the shock of the F- Vaguely Sauntering Downwards wore off. But Aziraphale isn't always there and it's not like She responded to his questions up in heaven anyway. Sometimes they were very serious like, "why is there so much suffering?" and "why are humans so much better at torture than demons?" and sometimes they were the flippant questions that made him unwelcome in hell and earned him those hidden amused looks of Aziraphale's that he liked to draw out. Like, what was up with dolphins? They were bastards, but because they were cute and funny, humans loved them (Crowley liked them too, for totally opposite reasons). And like, humans invented writing so he invented bureaucracy to torment them. But instead, both Heaven and Hell jumped on the bandwagon faster than the beany baby craze. Surely, if they were opposing sides, they couldn't both use bureaucracy?
(He is pretty sure he spent a year drunk on rice wine complaining about this to Aziraphale during China's Warring States period, but since Aziraphale had just discovered the Chinese classics, he's also pretty sure that Aziraphale didn't hear a word he said.)
Asking questions is Crowley's thing, even though there are some that he will never, ever voice out loud. Questions like, "when did it become more important to make my angel smile than to tempt a few humans into darkness?" and "at what precise moment did Aziraphale decide to add worrying about Crowley's punishment to his list of worries about heaven and hell, and could Crowley do whatever he did again to cause that reaction?"
Crowley isn't afraid of any questions, but he is sometimes afraid of answers. He fears that one day the answer will be, "never talk to me again," and "we need to stop." So he cowardly avoids any questions that might have those answers.
He often gets ordered to tempt the Israelites (or the Jews as they were coming to be called). They were God's chosen people after all. Though one question Crowley often asks is why God's chosen people are marked out for so much suffering? This is, unsurprisingly, a question the Jews ask too. In fact, it seems to be part of their traditions to ask an awful lot of questions of God as Crowley finds out when he ends up in a twelve hour debate with a few rabbis in Persia.
One of the rabbi feasts them afterwards, though Crowley is more interested in the wine. Rabbi M- something or other, approaches him after quite a few jars of wine have passed.
"I did not realize demons could be Jewish."
Crowley hadn't exactly been hiding his eyes, and around hour six of the debate may have forgotten entirely to tone them down for human consumption, so the demon part is hardly a surprise, but, "I'm not Jewish."
The rabbi places a comradely hand on his shoulder. "Ah, but it is very Jewish to ask questions, especially those that have no answers. How long have you been asking these questions?"
Forever. Since I can remember. He swallows those words down like the serpent he is. The rabbi just squeezes his shoulder, and smiles. Abruptly Crowley is enraged – at the Jews, at God, at himself.
He decides that the wine really isn't up to his stands (and Aziraphale would agree with him, so there!), and it is time for him to leave. Macedonia will be crazy in a century or two and he wouldn't want to miss it. He resolves to only do his job around the Jews, and otherwise stay far away.
However, he can't stay mad at them because they enshrine a man's comeuppance complete with silly hat into their religion and eat said hat in mockery every year – that is the kind of pettiness Crowley can get behind.