Korean people tend to think 죄송합니다 is more polite than 미안합니다. one might want to use 미안합니다 with strangers that look younger than them, but they would definitely use 죄송합니다 with their boss, teacher, a stranger, or a clerk would say it to a customer...
You're talking about politeness levels right here. Anyways, you're correct about friends saying 미안해 instead of 미안합니다 since the ending '니다' is used in polite/formal speech
I've actually heard 죄송해요 used. It was in a drama, but it was used to show a deep apoplogy. Although that's the case, theyre simply not common. What I've learn from my 선생님 is that there are certain words that are always in the formal form. 죄송합니다 being one of them.
Some words are just used more than others. 죄송합니다 and 죄송해요 are ways to say sorry in formal Korean and are relatively popular depending on the situation, but 죄송해 isn't often used. A more comfortable or natural means to say sorry in informal Korean would be 미안해