my imac runs macOS high sierra,what i am not getting is why the firewall doen't work, and my apple account won't sign in, or any of my other accounts(even including my google account) will not allow system services sign in
The final release of your version of macOS was released about seven years ago. It is well obsolete and support for it has evaporated. Secure internet access with a browser is no longer possible because security standards have changed over the years.
Most email services, including Gmail and other Google services will no longer work.
My friend, it's past time that you ditch that OS for something newer. If your iMac is a late-2012 model or newer then you may be able to upgrade the OS beyond High Sierra.
why would macOS not allow the firewall to turn on?
