"No, we are not eating anymore."
Translation:Hayır, biz artık yemiyoruz.
My understanding is that "artık" has to do with a turning point, a division in time connected to a change. So it could mean "anymore" (in the past it was this way -> now it is not this way anymore) but it could also mean "from now on" (in the past it was not this way -> from now on it will be this way) or "already."
"Şimdi" means simply "now," the moment of speaking