It depends on whom you are talking to. It’s never wrong to be polite and your first sentence doesn’t seem “very” formal to me.

Hi Arslan, I am a native English speaker in Australia. I understand what you are saying here, but I don't think it's a good idea to tell people learning English about "gonna, dunno, gotta". In my opinion that is very lazy English, commonly used in the USA but, for example, I would never walk into a job interview and say "My bad, traffic was crazy". And I definitely would never use any of those words in written English. "I'm going" is better than "I'm gonna go"; "I don't know" is just as fast as "I dunno"; and "I need to go" is just as fast as "I gotta go". Sorry, it's just my opinion, but I think these words might confuse people learning English. cheers, David :-)