All three of the choices are possible, depending on your ingenuity.

 

You get the answers to the questions you ask.
A nice exercise in brevity.

 

Professor Wikipedia does not recognize any such thing as a 'parallel plate sensor'. FWIW, nor do I. For a start, what material are the plates in? Liquid? Gas? Solids? Fluidized solids? Wheat? Outer space? It matters.

 

The TS may be interested in reading a NASA investigation of capacitance for proximity detection. Here is just one link: https://ntrs.nasa.gov/search.jsp?R=19930045105

I have also attached a pdf with more technical details. There is an appendix to that report that is much larger (about 3.2 MB) that I can't upload. If interested, you might be able to still find it on the web. I made one like this a little over 10 years ago: