I will be moving soon, but am not sure when I will receive my I-821.If I call Immigration Services and notify them about the new address I will live in, can that slow down the process of the action?

You must submit form AR-11, can be done online here: https://egov.uscis.gov/crisgwi/go?action=coa.Terms

Make sure you have mail forward to new address. Go to nearest post office or do it online here: https://moversguide.usps.com/icoa/icoa-main-flow.do?execution=e1s1&_flowId=icoa-main-flow&referral=UMOVE