need help...

Hi there I am new to the rotary world and to this forum
after selling my mr2 turbo I have just bought a 04 231 rx8 from the UK (114000 miles with a rebuild at 100000 ) the seller said it had a remap but no proof of that. It now lives in France


and i'm already having a little trouble with it and would really appreciate a little help from some experts !!


(i dont know if i am on the right thread or not??)
please let me know if I am not !


so here goes..


im having a hard time starting it (cold or hot) very unusual for a 8...
from cold starts i need to turn it over about 6 to 8 seconds for it to start (sometimes get a bang like a shotgun from the exhaust) then it starts
idle doesnt sound quite right and the car sometimes vibrates.


once warm it drives well with plenty of power.
when it comes to a hot start sometimes it will start after about 5 seconds and other times it takes about two 10second attempts.


the engine light came on with the Po 420 code = Catalyst System Efficiency Below Threshold (Bank 1)
it has the N3Z1 starter on it, new plugs i have just ordered new coils as no proof of last change


I cant bear to think of compression :(


any thoughts?? or tips would REALLY be apreiated


Thanks.