Image one: That's simply an icon representing the external drive you bought, there should be another one named "TM Ext HD Backup". It should not have the same colors as the SD drive, Apple makes it mostly green with the same TM 'circle' icon that is the trademark for Time Machine. Other external drives usually have the generic yellowish icon. There's not really any point in double-clicking any drive icon as all that does is open a Finder window to display what's in the drive.
Image two: I don't use SD any more, so I can't recall what "Smart Backup" does, exactly. OTOH, U don't understand why it shows five backups on 2/21 yet it shows the last backup before you bought the external drive. That is simply not logical. It appears that the last time you actually used SD was 6/5 last year?
OTOH, the Get Info image shows that the drive was "Modified" on 2/15. That may be factual, if SD found nothing had changed on your internal drive since that date.
Image three: What version of Disk Utility are you running? Mine is Version 15.0 (1511.3.1)
16.3 (1579.1) and, as Jon mentioned, it does not indicate types of files (Apps, Photos, etc.), it only shows Used, Purgeable and Free. Sorry for the confusion. I thought you had updated the OS. I think you are still using 10.11.6, El Capitan. The version on that OS does, indeed, have the "types" display. In other words: Image three is normal.
BTW, it appears that you have not used the "Journaled" formatting. It's not absolutely required and your main (internal) drive should use that.
Image four: Again, looks normal. However, could you give us a screen shot of you internal drive in either DU or the Get Info window. It should show roughly the same amount of disk space used as shown on the SD backup (~91GB).
Lastly, click the 'eject' button next to the .dmg labeled item in the left-hand section of a Finder window under the "Devices" area. If you don't see a "left-hand section", you can use the Finder->View->Show Sidebar menu item to... show the Sidebar!

[attachment=3517:TS_eject_drive.jpg]
If you don't see a list of Devices, click the "Devices" label area to display it:
[attachment=3518:TS_Devices_area.gif]
You can also just drag the item to the Trash, of course. I prefer not to put things in the Trash as a general habit. Only drag things to the trash if you intend to Empty the Trash as soon as possible. Too many things have been put in the Trash as a 'temporary' storage place and then erased when the person forgot to put it somewhere more useful. At our house, we rarely take stuff out of the trash once we put it in there!
