People do get EFCs of 0, it's difficult to know if you made a mistake without knowing some basics about your parents income and assets, and even then, there are many other factors that go into determining your EFC.
As far as how much Adelphi will give you in FA, there are a couple of basic questions to start with: does Adelphi use the Profile as well, and does Adelphi provide 100% of financial need?
If it uses the Profile, your institutional EFC could be considerably higher than your federal EFC.
If Adelphi does not meet 100% of need, there may be a gap between what they give you in merit + FA and the COA. Also, remember, FA packages are a combination of grants, loans and work study. BTW, if tuition is 23k, then your total COA is likely going to be more like 38k.