I have a wheel just like yours, and also attempted to take the freewheel off to make it fixed. The way I took it off was to pry off the dustcover, take out the ball bearings, and unscrew the cone using a flat screwdriver and hammer.
As you can see from the attached pic, the freewheel mechanism is a part of the hub. So unfortunately, it can't be used for a fixed gear. It's best if you just leave the freewheel like it is, and get a new hub.