Why does box 20 - locality name have all asteriks?

I assume that means that boxes 18 and 19 have values in them, but for whatever reason, the employer could not make an entry in box 20. If box 19 is empty, then you can safely delete boxes 18 and 20.

You're correct. Box 18 is empty, but box 19 has information in it. Would my employer be able to provide me with the locality name? 

Yes, your employer withheld and paid that tax, so your employer should know which locality they paid. 

It most likely is the city in which you work or live.