if nominative is normalny and instrumental is normalnym
then why is normalny used with jestem?
You use Intrumental with adjective + noun (they both are used in Instrumental) but Nominative if there is only an adjective.
You use the instrumental specifically when you're defining something, not just any time you use "być". For instance, you say "Tam są drzwi", and not "Tam są drzwiami", because you're not defining. You only use the instrumental when you say "A = B", as in "Jestem chłopcem".
It should be "Jestem nienormalny". In Polish "nie" with adjectives is written together ("nie" is treated as a prefix).
Regular in what? :D
I'd translate "I'm a regular guy" to "Jestem normalnym/zwyczajnym facetem", but I think it would sounds quite strange here, seems more of a fixed phrase.
No. "Jestem normalny" just means that I am a normal person, I don't think 'casual' suits the meaning.