I have Teamviewer 14 on my Mac.
I have the 'keep me logged in' setting set but every time I open Teamviewer it is asking for my password.
Not the password for a remote system, just the account password.
There are two situation we need to distinguish.
I hope this could help. If not, do not hesitate to ask your questions here.
If the Mac was restarted and Teamviewer is asking for the login info, is the Mac still available to be remote accessed ?
You only need to be logged into your TeamViewer account on the master side of the connection. Not on the remote side.
If your Mac is the device that need to be remotely accessed, then you need to use the Wake-On-Lan. This will allow you to shut it down and to turn it on remotely.
You will find all the information you need in our Knowledge Base article here: How does Wake-on-LAN (WOL) with TeamViewer work?
I hope this could help.