How to use CMD to backup files to .zip for archive : So this one's a multi-parter (Windows 7)

I have a folder structure as so:

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    C:
      SyncFolder
        Backups
      [User]
        FolderA
          Subfolder1
          Subfolder2
        FolderB
          Subfolder3

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My aim is to use the folder 'SyncFolder' as a backup system for certain files (Sync folder is actually a folder placed there by a file syncing service).

At present, I have the following within the Sync folder:

 - a .bat file containing a ROBOCOPY command (which copies 1 file)
 - a .vbs file which is used to call the .bat file (to avoid the CMD window appearing). This VBS file is being called once per hour by Windows Task Scheduler
 - the file which is being copied

So here are my questions:

 I'm looking for a code (preferably an edit to the existing .bat, as I'm not overly-technical) which can:

 - Copy Subfolder1 in its entirety into a .zip file, which is named YYYYMMDDHHMM_SubFolder1_Backup (where the date & time is automatically populated)
 - Move the newly-created .zip file to SyncFolder\Backups (or create it there in the first place?)
 - Deletes (or overwrites?) the previous backup
 - Repeats for each Subfolder specified (perhaps as an additional command line?)
 - Logs the details of the backup to a .log file located in SyncFolder (i.e. Name of .zip created, Date&Time of backup, size of .zip created)

**I'm aware this might be a bit ambitious for CMD or a .bat, but I'm open to any suggestions, but please do bear in mind that I'm not highly technical, so any walk-throughs would be immensely appreciated!**