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To answer the question regarding the feasibility of using incineration for disposal of plastics and other combustible waste, I suggest that you look into the medical incinerator designs developed by Jim Picken's team at de Montford university:
https://www.mw-incinerator.info/en/101_welcome.html
These incinerators have been demonstrated to generate reasonably low concentrations of noxious gases and have been successfully used in medical facilities around the world. However, this is clearly not the most environmentally sound solution as recycling will be preferable.
Regarding disposal of biodegradable material, simple composting may be more appropriate than vermicomposting.