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All the stuff and requirements that you write about (custom spatial and attribute queries, basic symbolization based on attributes, time animation), are standard functionalities of ArcGIS and QGIS, or available through commonly used plugins (e.g. TimeManager for QGIS). There is no need to go down to the PostGIS database level to do this, or to install ...
Although it's not Python based, you should better use geojson-join package. It works for JSON, CSV or DBF and it uses the command line. No need to code here except if you have a particular purpose I'm unaware.
It might be easiest to try using QGIS and dropping the geojson into it. Then do a join by attribute. A side benefit of it being graphical is that you can browse/label the counties and then quite easily spot check your joined data.
basically you could reclassify your image and directly read the pixel count in the raster attribute table. Multiplying count by pixel size would give you the area. As mentioned by @whuber, this assume that you are using an equal area projection (which should also be the case if you work with vectors).
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