"I'll be back."
Different form of "future tenses". There are 4 future tenses in all. But to answer to your question:
+ (으)ᄅ 거에요 - Probable future
+ 겠다 - Presumptive future.
Adjective/Verb + 겠다 when the will/intention is stronger.
Use in 1st person, declarative mood like in this case, it is more a matter-of-fact statement.
The conveyance of "assured intention" is only one of the uses of 겠다.
I know this is 2 years late BUT 가다오다 verb means more like you went to do something and then came back. So like for example:
학교에 벌써 갔다 왔니? You've already been to school? (Lit. You already went and came back from school?)
I don't think I've ever seen these two verbs used together in any other case but past tense. I could be wrong though and someone else explain it to you.
The difference between 저 and 나 is not in the level of politeness.
저 is an expression of humility, the 'humble, I'. 나 is more of a 'neutral, I'; hence it is sometimes interpreted as being more removed, sometimes as casual. Their use is situational.
Do keep in mind that over-formal/humble can be perceived as sarcastic; and over casual, as rude.
In this case, with the use of the verb in plain (neutral) form, 돌아올 겠다, it is inapt to use 저 because the speech is not directed at any specific individual(s).