Not sure what you refer to as ungroup. Could you elaborate? To get out of Object mode select an object and hit the tab key.

If everything is part of the same mesh, you can go to edit mode by selecting the object and hitting the tab key and separate the parts there.  If all the pieces you want to ungroup are completely separate (no shared vertices between them) you can just hit the p key and select "separate all loose parts."  The parts that are not separate you will have to select individually, hit the p key and separate the selected parts.

I would recommend naming items, it makes them easier to find later, but it is not necessary.

BTW, you can also get out of object mode by using the mode menu on the 3d view window.  In your screenshot there is a white box on the menu bar under your 3d view that says "Object Mode"--that's a drop down menu that lets you select other modes like edit mode, pose mode, uv face select, etc.

The TAB key has an interesting property - well, interesting to me, anyway. I always thought it was the shortcut key to get in and out of Edit versus Object mode... and it does, but it's actually a toggle between whatever the last two modes were that you've been using.

I know: "Thank You, Captain Obvious!" - Hey, it was a new discovery to me...    :-)

The tab key worn down from hitting it - just kidding! even the drop down list under Object has no other option. I tried hitting the p-key, but then everything on the blender view disappeared, had to restart just to get back in - I won't be using the P key anymore until later. Will march on to victory

The only time I've had something like that happen is when I actually had a dialog open that couldn't see because the region associated with that dialog was shrunk to nothing - the only clue I had that a dialog was active was that the panel options had changed. Weirded me out until I realized that was what was happening. And yes, TAB did bugger-all...