There could be may reasons for unstable rpm...
IACV, TPS, etc... but as you said these problems arouse after tappets adjustments them they could be the problem...and getting tappets adjusted is the cheapest start towards solving your problem...
For White smoke...it could be also from tight tappets...when tappets are too tight they dont allow valves to close fully which cause oil to drip into the cylinders causing white smoke...problem is much more evident when cars is started after few hours interval....
Get tappets adjusted...hopefully this will solve both your problems...