Would a domestic violence case when I was 16 affect me if I applied for the dream act?

It may impact your application. You need to consult with an attorney before filing.

Any criminal related case may have an impact on applications submitted before the USCIS. You would be best served by investing in a consultation with an experienced Immigration Attorney who can review all of the details of your case not just this one matter. Many like myself, will even do these over the telephone to accommodate clients. Immigration law is Federal, so any qualified attorney should be able to assist. Call one of us BEFORE you do anything that may put yourself in a bad situation.

There is no Dream Act and I assume you were referring to Deferred Action for Childhood Arrivals "DACA" instead. Responding to your question, if you were convicted of a crime constituting the crime of domestic violence, it is highly likely CIS may not extend discretion to you if you request for benefits under DACA. I note you mentioned the crime took place while you were 16 years old and as such, you may have been treated as a juvenile and that record may have been sealed. You should speak to a criminal lawyer in conjunction with an immigration lawyer to explore your options.

It can but you can be approved too since it does not count as a conviction since it would be a juvenile matter.

It might. Were you convicted? Were you tried in a juvenile court?