"Believe", in a faith without proof sense, is shinjiru 信じる in Japanese. As in English, this is a lot stronger than mere thinking.
Omou is used a lot in Japanese as a politeness marker of sorts: instead of stating flat out that the moon is green cheese (tsuki ha guriin chiizu desu), you soften the statement a bit saying that you think it's green cheese (tsuki ha guriin chiizu da to omoimasu). When translating to English, you'd often drop it entirely or at least find other ways to express it, because in English it's not natural to tack "I think" to everything you say.
Sure. Creer is very often used in a similar way to tacking on to omou to express best guess/subjectivity/lack of definition. Kirei [da] to omou can be pretty close to Creo que es bonito for thinking something is pretty.
I'm not saying it's one-to-one, just the same kind of issue and you'll see very similar conversations about both. Therefore, it feels familiar and not astounding per Iyer.
Omou is used a lot in Japanese as a politeness marker of sorts: instead of stating flat out that the moon is green cheese (tsuki ha guriin chiizu desu), you soften the statement a bit saying that you think it's green cheese (tsuki ha guriin chiizu da to omoimasu). When translating to English, you'd often drop it entirely or at least find other ways to express it, because in English it's not natural to tack "I think" to everything you say.