It's better to buy a cleaning fluid for lens filter. 

I don't see why not, remember that the filter goes on the lens, not on the camera. 

The adapter clicks on the lens. It has a small dark gray colored lever (not the white plastic tab to change aperture), level to the outer edge of the bottom ring accessible when removed from the camera, grab the whole adapter with your left hand and push the lever in with your thumb, and while pushing, rotate the lens with your right hand to remove it. You need to push in that lever to unlock the lens. 

pull back the lever and twist the adapter clockwise (from the back of the lens) 

There is no need to deliberately tidy it up. The only purpose of the reflector is to push light into the shadows, so having wrinkles will not affect its use.