Before Carisi leaves the bodega, he puts his wedding ring back on. He leaves the building and hugs Amanda (his wife). With the camera positioned behind Amanda, Carisi's hands are shown on her back and showing no wedding ring.
After applying pressure to the bullet wound Ollie suffered, Carisi gets up and then approaches the perpetrators with his hands raised. There is no blood on his hands, as there surely would be if they had been applying pressure to an open wound.
At several points Olivia tells the precinct commander, hostage negotiation detective and ESU officers what to do, as if she has the authority to give them orders. However this is not a sex crime or an SVU case, in hostage situations the local precinct commander and hostage negotiation detectives make the calls. That combined with the fact that the precinct commander is also a captain means Olivia would not be making the calls here.