wright two part question part one - will one of these 2o quid obd2 code readers work on a mk2 fiat punto 1.2 8v at all.

part 2- after replacing the engine with a new one changing pistons, rings, vavles seals plugs leads throttle body lamba sensor induction kit exhaust the car is still lumpy / misfiring on idle but perfect under load and driving at speed. as soon as it idles it starts hunting and missing. wen the engine is stone cold in the morning it revs up and straight down but once it warms up it revvs up holds there then comes down wen it feels like it my question is should a daashboard engine management light be on at all or isnt it gonna b a big problem. next is there any chance a map sensor would cause this its the only thing i havent changed yet as it was covered in oil from previous engine failure.
and lastly wen i took old engien appart it had melted to pistons and chucked out clouds of blue smoke from rear as it was burning oil. as there would of been fault codes in ecu does it need re3setting even tho i hav had battery off for 2 weeks does tht clear it ? sorry for long post i really dont know wot to do next p.s the car is a mk2 1.2 8v punto w reg 2000 plate

obd2 reader will be fine. The error code will need resetting else it will stay on.

Worth changing the map sensor, or making sure its properly degreased/cleaned