you live in PA, your employer should be withholding local municipality and PA state income taxes. That's what this form is for -- to tell the employer exactly where you live.

Yes, it is separate from the flat state tax. PA also has local taxes that are paid directly to the local municipality. You can look up your rate and tax collection agency here: https://munstats.pa.gov/public/findlocaltax.aspx

As someone who is originally from CA as well, local taxes were very odd to get used to.

Suppose you didn't do anything at all or filled it out incorrectly. When you sit down with your tax preparer at the end of the year they will make the correction. May involve waiting for a refund from wherever you overpaid. Inconvenience of time but ultimately a minor administrative correction.