"I'm sorry. It's okay."
Politeness level. 미안해 Doesn't have a politeness particle like 요 on the end, so i think it would be considered Banmal (casual language). 미안합니다 Is Jondenmal (formal language).
Can '괜찮습니다' also be translated as "I'm okay"? I don't see how these phrases denote a difference between I/it
Yes, it can, depending on context. But it's more used after someone, for example, bumped into you and says sorry (similar to this sentence here). But 괜찮아요 is a very versatile expression.
First of all, it's 괜찮아[요]. Second of all, it's not always "I". Korean is a context-dependant language. It can mean everything from "I am okay" aaaall the way down to "They're okay". It just depends on the context of the situation.
I don't know but I'm pretty sure on this speech level we have to use formal ending "습니다" with "스" dropping after a vowel and that's why it could've considered your answer wrong
Although that's technically correct because you're using the correct words, you're mixing both levels of formality, so your grammar is incorrect.
미안해 is the "declarative present informal low" form of the informal word for sorry
죄송합니다 is the "declarative present formal high" form of the formal word for sorry