I think you are going to have to put a little support structure in there but I'm not certain you need it.
On the slicing issues - somewhere burried in the advanced features is something called "fix horrible A" I believe. Uncheck that - that is party what is causing your "plate".
What CAD software are you using? Is this from sketchup? If so you have to make ti manifold (link at the end).
Tell me more about the missing layer - look at this area in xray mode. It sounds like your model is not manifold. A manifold model can be filled with water. Your model may have holes in it or may have inner walls.
More on sketchup and manifold (if you don't use sketchup skip to #4 and #5 sections of this link):
Make a square surrounding the structure so each layer takes more time and the pla can cool down properly. Other fast fix, put a small fan in front of the printer to increase the air cooling. When doing small areas, pla must cool down. The standard fans have its limits on cfm, to avoid them you can use Labern fancap (youmagine) to have better air on the print, or just bruteforce it with a small fan cooling down the print.
Also maybe 190C & 20mm/s can be too hot for that speed. You can, if you want, change the temperature in the middle, using change at Z (or something like that plugging), or manually edit the gcode to add speed slowdown at certain point of your print.
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