Does the F11 key just have 'F11' written on it, or are there other symbols? If so, you may need to hold the 'function' key (often written 'fn' and located next to Ctrl and in a different colour) and press F11 at the same time.
When you say 'brings me back to you', do you mean it changes the website you're looking at?
Also, the bar that should appear at the bottom (and probably the bar that had the icons you are missing; Word, Skype, etc.) is called the 'taskbar'. Has the taskbar been visible at all during this? Is it the taskbar's disappearance that you are referring to when saying "I cannot see the buttons at the bottom where I can open things. Lots of changes lately. Cannot see Sykp and more."
Make sure you click on empty space on a website, then press F11 (take care to press it once). The taskbar should return. F11 is a universal key for 'full-screen mode' where a single window will cover the entire display, rather than allowing the taskbar and Window control buttons to appear. After pressing F11 and going into full-screen mode, you should be able to restore the taskbar by pressing F11 again.