I haven't found a direct reference to this, so I'm not sure how this works. After installing and booting tails, if I use the Synaptic package manager to find, and install updates, are those updates actually installed on the boot device so they are present next time I boot? Or only to the Live image, so they are gone as soon as I reboot, and need to be downloaded/updated again next time I boot?
And is it advisable to run the synaptic package manager to update? Or is it presumed that one should always use the official tails ISO image ONLY?

If you update your packages, as when you install a new package, they will not be automatically reinstalled at the next reboot.
Please also note that updating packages can make it easier to differ you from other users, and so break your anonymity.