Welcome to the forum. Newer versions of Ghost for quite some time do not use the .gho extension, this was for much older versions of Ghost. The newer versions all use .v2i extensions for image backups.
Are you creating a Backup My Computer job to create an image backup or doing a File and Folder backup? In Ghost 15 you define a backup destination and that can be your external USB drive or whatever drive you choose.
Please see chapter 6 of the Ghost 15 users guide for details.
"Backup my computer" will create an image of your hard drive. It will be stored as a .v2i file, not as a .gho file.
Go to Tasks > Run or Manage Backups > Define New. Select Backup my computer and go through the steps to create a backup job.
Alternatively, go to Tasks > One Time Backup and follow the steps to create and run a one-time backup.
In either case, I strongly urge that you follow AllenM's advice and take the time to read chapter 6 of the user guide. Ghost provides numerous options for running various forms of backups and their selection will depend on exactly what you want to achieve.
How are things going? Please configure the backup job as outlined in Chapter 6 of the Ghost 15 user guide. If there are any questions you have related to setting this up as you are going through it please post them and I will be happy to address them.
Thanks for the update. Ghost uses VSS (Volume Shadow Copy Service) so that any VSS aware database application, etc will be stopped during the backup and started back up when the backup is complete. This allows for any database application to be left in a sane, unchanging state to ensure the backup is consistent.
If you have a NON VSS aware application it can be shut down by using scripts which Ghost can call before starting the backup and started back up when the backup job is complete.
I have never heard of a problem doing a hot backup and ultimate restore with Ghost.
Be aware that Ghost 15 does also allow for a COLD backup which can be done from the recovery environment if you so choose.