What is the correct way of the following two options?
1) I'm gonna listen it
2) I'm gonna TO listen it
gonna = going to.
If you use the second one, you'll say
I'm going to to listen it.
But you need to use listen to, so you get
I'm gonna listen to it.
gonna comes from "goin' 'a" which leaves a couple consonants out of "going ta" which is what "going to" sounds like in some informal speech.
So, "gonna to" is "going to to" and doesn't make sense.
Similarly, "wanna" is "wan' 'a" which is "want ta" and means "want to."