Why is my external flash (speedlight) not working on-camera?

I would like to use external flash with my Olympus OM-D E-M10 (mark I). It seems, however, that flash is simply not working with my camera. I have tried to set flash in camera to fill-in and fully manual mode, but no luck at all. Also I have tried different modes on external flash itself, including fully manual.

The external flash is Neewer Speedlight NW985. The only mode which is working is the wireless one where flash is triggered by in-camera flash.

What I can do to make the flash working? Is OM-D compatible with any hot-shoe flash or not? Which flash should I get if not? Or is my camera just broken? (It is possible, I bought it on ebay)

Also it’s interesting that in the moment I connect flash into hot shoe of my camera, it fires. Is this normal?

I am total flash-newbie, please be patient. 🙂