Issue downloading High Sierra... error mssg after trying to add helper tool

Do you already have a copy or partial copy of High Sierra in the Applications folder? If so, then you need to put it in the Trash.

How to upgrade to macOS High Sierra (10.13)

Before You Upgrade macOS

1. Fix any problems before upgrading.
2. Run First Aid in Disk Utility while booted from your Recovery HD.
3. Backup. Make a bootable clone using CarbonCopy Cloner or use TimeMachine.
4. Be sure your startup disk has 18-20GB of free space during the installation.
5. Upgrade third-party software for compatibility. See App Compatibility Table - RoaringApps. If you have mission critical software, then DO NOT upgrade until you know that software is compatible with the version of macOS you are about to install.
6. Disconnect all third-party peripherals.
7. Download the installer which will be in the Applications folder. Quit the installer after it opens, then make a copy of the installer and save it in the Downloads folder. The one in the Applications folder will be deleted after a successful installation.
8. The download is large, anywhere between 5 and 9GBs. It takes time to complete. Be patient.
9. Double-click on the installer in the Applications folder. Click on the start button to begin the installation.

Sometimes it may be better to run the installer from Safe Mode.

Installing An Upgrade From Safe Mode

1. Disconnect all peripherals connected.
2. Reset your Mac's PRAM and NVRAM.
3. Restart the computer and immediately, at or before the chime, press and hold down the Command and R keys until the Utility Menu appears.
4. Select Disk Utility and press the Continue button.
5. Then select the indented (usually, Macintosh HD) volume entry from the side list. 
6. Click on the First Aid tab in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
7. Select Restart from the Apple menu. Press and hold down Command-S to start in Safe Mode. This is slower than a normal startup. Don't panic.
8. Now, try installing the upgrade and see if you have normal results.

Bootable USB Installers for OS X Mavericks, Yosemite, El Capitan, and Sierra

First, review this introductory article: Create a bootable installer for macOS. Second, read this How To outline for creating a bootable macOS installer. Simply use the Terminal command by copying and pasting the command line for the version of macOS from the list below. You will need an 8GB or larger USB flash drive that has been partitioned and formatted for use with OS X as well as an installer for the desired macOS version that you have previously downloaded from the App Store.

Drive Partition and Format

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the drive (out-dented entry with the w/type and size info) from the side list.
3. Click on the Erase button in the Disk Utility toolbar. Name the drive, "MyVolume". <---- IMPORTANT!
4. In the drop down panel set the partition scheme to GUID. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button and wait for the Done button to activate. When it does click on it.
6. Quit Disk Utility.

Create Installer

Open the Terminal in the Utilities' folder. Choose the appropriate command line (begins with "sudo") depending upon what OS X installer you want. Paste that entire command line from below at the Terminal's prompt:

Command for macOS Catalina:

sudo /Applications/Install\ macOS\ Catalina.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Command for macOS Mojave:

sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Command for macOS High Sierra:

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

Command for macOS Sierra:

sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ Sierra.app

Command for El Capitan:

sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app

Command for Yosemite:

sudo /Applications/Install\ OS\ X\ Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ Yosemite.app

Command for Mavericks:

sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ Mavericks.app

Press RETURN. You will be asked for your admin password. It will not echo to the Terminal window. Then press RETURN again. Wait for the return of the Terminal prompt signifying the process has completed. It takes quite some time to finish. Be patient.

The bootable installer can be used to install the selected version of macOS. Shut the computer down. Insert your flash drive into a USB port. Start the computer like so:

Boot Using OPTION key

1. Restart the computer.
2. Immediately after the chime press and hold down the  "OPTION" key.
3. Release the key when the Boot Manager screen appears.
4. Select the disk icon for the USB flash drive.
5. Click on the arrow button under the disk icon.

Sorry about the link. That must have changed recently. Here's the proper one: Reset NVRAM or PRAM on your Mac - Apple Support.

Download the installer which will be in the Applications folder. Quit the installer after it opens, then make a copy of the installer and save it in the Downloads folder. The one in the Applications folder will be deleted after a successful installation. It makes sense if you read the entire line that was posted. 😀

Yes, run the installer that is located in the Applications folder.

Have you verified that your model can be upgraded to High Sierra? Are you logged into an Admin user account?

I think this goes back to the original problem. I believe you have a bad download of the Mojave installer. I suggest that you put the installer you have in the Trash. Re-download Mojave from the App Store or one of the following links:

https://itunes.apple.com/app/macos-mojave/id1398502828?mt=12

https://apps.apple.com/app/id1398502828?mt=12

Then give it another try. Be sure to use Disk Utility to run First Aid on the target disk before the installation. Also, disconnect all third-party peripherals.

This will be my last for the day since it's time to watch today's news. I may be back later tonight.

Saving the installer means you don't have to re-download it should you need to reinstall it. Just a convenience and lessens the time needed when you do need a reinstall.

Question: If you notice, that grey circle "timer" on the right side of the file name shows it not complete. Even after it completely downloads the actual installer file, it still remains like that, an incomplete circle, with a "wedge" missing. Is it supposed to be like this or does that indicate a problem with the "macOS Mojave.appdownload" file?

That is, indeed, a download completion indicator. When the download is properly completed, then the indicator disappears and the filename is changed to "Install macOS Mojave.app". It should start up automatically and present the startup window. Click a button to start the installer. Or you can use Command-Q to quit the installer. Later you can start the installer by double-clicking on the installer in the Applications folder.

If this is not what is happening, then there is a problem. Unfortunately, what the problem is will not be easy to determine.

3) I double click the "Install macOS Mojave.app", it runs for maybe 15-20 minutes downloading, then it stops and gives me the same error message:

If there is no problem at this point, then it only takes minutes to download the needed files. As long as it runs for you suggests there is a problem. It could be your Internet connection or a problem with your startup disk.

My suggestion is that you try to create a bootable USB flash drive installer while you still have the installer app sitting in your Applications folder. Instructions on doing this will follow.