It's not common for people to say that in a sentence. I don't think I have ever heard anyone say that exactly. It's not standard English. But I have heard people say things like that as a part of a slang phrase. Example: When a person feels overwhelmed by work, social and family obligations and needs more time for themselves to relax and nurture themselves they might say something like: "I'm so tired of doing everything for everyone else. I need some time to do things for myself" (Standard English) "I'm so tired of doing everything for everyone else. I need some me time" (English Slang ) I could imagine someone using "there is no me now" in this way: Example: A woman recently got married and is finding it hard to maintain a sense of personal identity. "I am happy to be married but it's strange. I feel I have lost my sense of individuality. Now I just see myself as part of a couple." (Standard English) "I am happy to be married but it's strange. There is no me now. There is just us." (English Slang ) "There is no me now" is not commonly used in standard English but I can see it being used in English slang, in the lines of a script for a play, in the lines of a poem, or in the lyrics of a song.

No, it's not normal. Without context, it doesn't really make any sense. (I can't tell what the speaker means.) I assume you heard it somewhere. If so, the context probably explains what the speaker means by "no me."

It is not a sentence I would hear in normal conversation

I think no you cant use it like this