Could you use this as a (casual) greeting? (In German, you sometimes just say "Tag!" ("day!") to greet someone)
Yes, but only if you put "god" in front of it, like "God dag!", which directly translates to "Good day".
Is the pronunciation correct? I wouldn't know, but knowing that "jag" rhymes with the English "guy," should this sound like that, or is the present pronunciation (like the English "dog") correct?
Err, 'jeg' (I) rhymes with guy (http://forvo.com/word/jeg/#no). The only reference I find to 'jag' is here: https://en.wiktionary.org/wiki/jag#Norwegian_Bokm.C3.A5l . And the recording does sound like 'yog'. For some reason there seems to be lack of good recordings of "dag" or even an IPA pronunciation. But I believe you can hear it well here: http://forvo.com/word/en_fin_dag/#no .