Which synamorphy evolved last
A cladogram does not indicate time. That would be a calibrated phylogram. We can tell from the above cladogram that the two synapomorphies "Hair" and "Eggs" with shells are the two most recent, and happened after all the other ones because cladograms do indicate the relative timing of events. However, knowing a bit about mammals, "Hair" is the more recent than eggs with shells. Actually, eggs with shells should be on the same internode as "Amniotic eggs" in this cladogram, because Montreme mammals had eggs with shells, which were lost in the most recent common ancestor of Marsupials and Eutherians (Primates and Rodents/Rabbits are both Eutherians). So "eggs with shells" came first.