Having successfully installed Zorin, I find that if my computer 'blacks out' while I leave it unattended for a few moments, when I try to unlock it, it wants a password other than my sign in password. Furthermore, when I try to download software (to install skype) it tells me I do not have privileges and demands a password that I have certainly never given it.
The only advice I can give is to... REinstall Zorin OS.
Something must have been mis-recorded during your password creation.
You can set the amount of time that passes before the auto screenlock in your Power Settings- or set it to Never blank the screen.
Yes, just click on the logo bottom left of screen, then click on settings. From there go to POWER. And from there you can find your settings for POWER related stuff there.
Furthermore, if you go to PRIVACY, and then on the bottom tab from there, you will find options for your screenlock as well that you can also adjust there. There are also a few options you can adjust under DISPLAY in there too.
If you ever need to do even further modification that is not found in the Zorin system Settings, then you can....
T to enter Terminal.
sudo apt install gnome-tweaks
When you launch tweaks, you will find further custimization that you can do in there.
If you are referring to the dialogue asking for root or admin password, you did supply it. When you create your account, your account is added to the sudo (super user do) file and group. When it asks for a root password or administrator password, your account password will be what you use.
In Windows, if there is only one account on a machine, it defaults to the admin group. The same applies in linux. Linux prompts requiring privilege escalation are not as "user" friendly, but are accurate in their request. It is asking for your account password every time those requests appear.