Can I claim 0 dependents on my W-4, buy claim 1 dependent ( myself ) on my 1040 ?

Yes,  The W-4 is for your employer to know what you want taken out of your paycheck in taxes.

You are not considered a dependent for yourself, so zero would be appropriate.

Yes.  What you enter on the W-4 that you give to your employer for withholding federal taxes from your wages has no bearing on the filing status you enter on your tax return