I think its possible your issues are related. What colour is the smoke when it burns oil for 10-20 seconds. It might not be oil it could be your carb mixture. Which could explain your idle issue. Have you rebuilt the carb? If not I would suggest doing so. Its possible that your rings are allowing bypass untill fully filled but very unlikely. I would check the carb and compression. Make sure the engine is stone cold when you pull compression.
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