Here's what I did on my Win8.1x64 laptop... File Explorer (on my system) will reopen the same way I closed it. If I maximize FE it will reopen maxed, if I stretch it to a particular size it reopens the same size. IIRC, I tested FE maximized and it survived a reboot meaning the setting was remembered.
I pinned File Explorer to the taskbar from what I guess is the Apps View from Start - where you sort apps by name, most used, etc. I right-clicked FE, I was presented with various options including Pin to Start, Pin to taskbar, I selected taskbar and an icon was placed on the taskbar.
I don't get the same options you get when right-clicking my taskbar icon, my options are -> File Explorer (to open), or Unpin the program (to remove). There may be differences depending on how you pin the app, from the .exe itself or from Apps View in Start, not sure just offering up the possibility.