Technically yes, but "I'm gonna" is sloppy English. If you use it, expect people to treat you as if you failed school.

I'm gonna means I am going to - but in a relaxed informal way. it is not the same as I am going. without to, I am going can do other things such as I am going somewhere. - I am going out. - I am going nowhere. These are different than I'm gonna- which is often an action besides traveling.

Means the same! Both is perfecto!

Yes.

In my opinion "I'm gonna" is not the same as I'm going. Gonna= going To. If you're saying you're leaving you don't say "I'm going to" you say "I'm going" or "I'm out" or even "Peace" or "Peace out" (We usually say this making a peace sign, like a V ^.^) I'm gonna is used more when you say you're going to do something. For example; "I'm gonna get cake" or "Gonna get you those shoes you wanted". In, "I'm gonna call you" you can also say "I'll call you". That's fine and you see how there you also could say, instead of gonna, Going to? Because that's what it basically means. Hope I helped :D