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As long as your shapes (edges of them) are actually AxisAligned the simplest way to draw it is to just draw multiple rectangles. They can overlay each other if they are the same color anyway. This can be as easy as drawing a 1x1 white texture with the desired Rectangle (Position,Size) and the required color. Your provided image would therefore consists of 4 ...
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I'm not sure, if I understand exactly what you are searching for but it would make your life a lot easier if you would use a grid of squares for the map. You could highlight different regions by simply changing the color of each grid peace that belongs to the area.
Regarding the outline: If you are using just one shape you should look into using Shaders for ...
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I'm not familiar with libgdx so the exact implementation in it is not something i could provide you. However, the concepts in play are pretty universal.
Assuming several things.
You only want to fill in the red area as that is how your question sort of reads.
You have the vertexes of the polygon you're looking to draw.
LibGDX cannot draw a concave polygon ...
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