Is it normal to have different withholding status for federal and state? Claimed 1 on W-4 (for self) but 0 on NYIT-204 bc directions state "do not include yourself."

First, your asked about "status" and then talked abut "exemptions".  As far as any of this is concerned the only important things is that you have enough withholding taken out to keep you out of a "penalty situation".  In number of states, you are required to use the numbers from your Federal W-4.  Other states have their own W-4 equivalent.  California (and a few other states) have more then 1 kind of exemption.  So, no it is not unusual to have a different number of exemptions between the Federal W-4 and the state equivalent.