Apple iMac automatically signs me out.

That is weird. Have you tried to restart the mac to see if the issues persist?

If they persist have you tried to boot the mac in the safe mode to see if the issues persist

1. On your Mac, choose Apple menu  > Shut Down.
2. Wait for your Mac to shut down completely. A Mac is completely shut down when the screen is black and any lights (including in the Touch Bar) are off.
3. Press and hold the power button on your Mac until “Loading startup options” appears.
4. Select a volume.
5. Press and hold the Shift key, then click Continue in Safe Mode.
6. The computer restarts automatically. When the login window appears, you should see “Safe Boot” in the menu bar.

if the issues do not persist in the safe mode they are most likely caused by an external piece of software

In addition to what WheelieNick suggested...

1) Check all of your iMac's power connections to make sure that none are loose.

2) If your using a Hot Corner to start screensaver or put display to sleep..?

Disable the Hot Corner or visit your Lock Screen settings and set "Require password after..." to Never.