I came to US at the age of 11 yrs old, green card holder and my Mom is a US Citizen. Will I still be able to apply for N-600 form even I'm 45 yrs old now?

So basically what you're asking is whether you are already a U.S. citizen. (N-600 is for getting proof for people who are already citizens.)

You didn't give exact dates, but given that you're 45 now, and you came at age 11, that must have been around 1981. And you must have turned 18 around 1988. Between 1978 and 2001, in order for a minor to automatically derive citizenship from the parents, both your parents must have naturalized while you were under 18, or if your parents were divorced or one of them died before you were 18, then the parent having sole custody had to have naturalized while you were under 18.