Sorry for the delay in replying.
I have to admit that I don't recognise the USB disk on any of those screen shots but then I have always used Zorin which is based on Ubuntu.
When I plug in a USB adapter mounted drive it appears on the desktop. Clicking on it opens it in the file manager (just like windows explorer), clicking on the drive in the left panel opens it in the right panel showing all the folders, then clicking on a folder opens it and displays the files. Once you can see and check the files are there you have two choices - you can either drag and drop individual files to where you want to save them or you can go back and drag the folders to where you want them saved (dragging folders includes the files in them.
It couldn't be easier. You can even plug in another USB adapter mounted drive and drag everything over to it, you then have a backup of your data.
Note: since your disks were setup as a RAID 1 array you only have one disk to copy(the two disks should be identical), the second can be used as a check disk in case any of the files on the first one are damaged.
Edit: I should mention that I have used a Zorin live DVD to do this type of recovery when there wasn't a Linux computer available.