Trying to Update my High Sierra and get Erro Message - Request time out (-1001)

Check that you have space on the drive to store the file.

Repair the Drive for El Capitan or Later

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the Device list. 
4. Click on the First Aid button in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

Try downloading macOS High Sierra 10.13.6 Combo Update.

You have a special problem with your current system and/or drive. How is the drive formatted? Check using Disk Utility. Your drive should use the GUID partition scheme and be formatted Mac OS Extended, Journaled. There should be two entries in Device list: An out-dented entry with the drive name and size; and an indented entry (startup volume,) usually, named "Macintosh HD."

If everything looks proper, then you need to reinstall macOS on the startup volume. You should be able to do the following:

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, "Macintosh HD") volume entry from the Device list. 
4. Click on the First Aid button in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Install OS X from the Utility Menu and click on the Continue button.

It's formatted APFS as indicated under the main heading, "Macintosh HD," where it say, "APFS Volume * APFS." I'm not sure what the problem is. It appears you are already running High Sierra. Perhaps, the error is due to not requiring the update. I'm not sure. The partition section is just informational, if you are attempting to create another partition or add a shared-space volume.

Are you sure you are running High Sierra and not Mojave? The former is 10.13.6. I think that is what you have indicated. There is nothing obvious that would prevent the update from installing.