Hi,
The Finder is running all the time.
You can click anywhere on the Desktop pic you have showing to make it the App that is then listed in the menu bar.
Baby Boomer may be dragging items from the Applications Folder to the Desktop.
Open a Finder window and navigate to the Application folder.
Use the bottom right hand corner to resize if required.
Click and hold an item and then drag it to it's new place.
The Desktop is really a full screen window in this case and you can just let go to place things there.
I feel Baby Boomer is not actually doing this but is creating (or has created) those Folders within the Applications and is using them to "sort" things.
Although you can change the size of the icons what you find works may be bigger than will display all your apps
In same cases "sorting folders" can help.
There are exceptions such as Messages, which will not update if it is placed in a "Messaging" folder.
Older versions of the OS were less fussy about this and you could keep applications almost anywhere.
Apple are getting stricter about this but I also talking about htis happening over 20 years.
The best thing is to just try things.
Another resource are Mac User Groups
9:18 pm Thursday; December 19, 2013
iMac 2.5Ghz 5i 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad