Re: "I am gonna go" vs "I gotta go"
It's certainly true we say "gonna" for "going to" but I can't imagine pairing it with the non-contracted "I am."
I'm gonna -- normal casual speech (non-standard in writing)
I am going to -- standard writing, somewhat more formal spech
I'm going to -- standard writing and standard speech
I am gonna -- odd combination in speech
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.