What is the difference between i hele dag and hele dagen?
"I hele dag" will always refer to today, while "hele dagen" is more versatile and can be used for other days as well.
Is it correct to use "i hele dagen"?
None, they are interchangeable
This does not necessarily mean outside in a literal sense. If I ask a colleague where hes been all day, he might answer with this sentence, meaning that hes been in a customer meeting all day (and thus, indoors, but outside of our office).
How do you say 'I've been out every day"?
"Jeg har vært ute hver dag."