The first part of your problem were you said once it got hot it hunts and shakes idle issues, sounds maybe like coilpack problem maybe ? if the engine is miss firing you will get the shake and odd idle,
But without seeing the car or looking at it only can give you my opinion
Hope you get it sorted out soon so you can enjoy your car
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Car's current and past
2014 Brz Love it!! 2010 Wrx cs10, 1994 gtst m spec 2004 Impreza RS,1998 typeX