These are separate and unrelated idiomatic expressions. The first implies the other person isn't paying attention, and can be phrased in various ways:
I feel like I'm talking to myself.
Am I just talking to myself or are you listening?
Oh yeah, you just finish that text while I stand here and talk to myself.
It's most often phrased as the present progressive to indicate an ongoing and immediate action, but it doesn't have to be. The important thing is to use it in a grammatically correct way, and in a context where it makes sense. It is possible to literally "talk to yourself" (which people do all the time) but in this context you want to imply that is not your intention, that you had expected the other person to be listening, but they are not.
The second expression implies that the other person or persons have no right to tell you that you are doing something wrong. Again, many possible phrases:
No one can judge me!
Don't judge me!
Stop judging me!
You have no right to judge me!
And so on. Most often it is expressed in the simple present to indicate a general principle, or a recurring action, but it doesn't have to be.
To answer your other question "What am I to talk to myself here" is not quite right. "Who am I to talk to myself here?" is better. Although I'm not quite sure what it might mean, it is grammatically correct and might make perfect sense in context.
Side note: Some ethnic vernaculars are known to phrase questions where other vernaculars would use statements. "Who am I to talk to myself here?" sounds like it would be one of those.