On windows: Press Tab key, or Tab key + Shift to see screen with Tool box
InDesign has a fullscreen mode which you get to by pressing Shift-W. But you can't work in that mode. It's more for presentations. (In fact, it's called Presentation mode.)
If you want to get rid of the red, yellow, green buttons, you want the documents to be set as tabs. You can drag them up to make tabs or go to Preferences > Interface > Open documents as tabs.
Perhaps with tabbed documents and using Shift-tab or tab you will get what you're looking for.
Someone is out now, trying to find a more obscure way to name "full window, but not full window" functionality.
You asked for a way to go into "full screen mode" and "full screen work mode." You never actually said "full window".
Please go to Acrobat, Photoshop, Quick Time Player, Skype, YouTube, Netflix, and Adobe Bridge and look what "Full Screen" means in any of those programs.
You ask for something, but use an incorrect term. Then, when we work hard to discern what it is you want, you get angry that the term you used was wrong.
Please, sir, think about your attitude. You insult Adobe and the people here who are trying to help. And the people here do so without renumeration.