ideling and turning off problem w/ my red top

[Id RaThEr DrIfT]

okay this all started happening lately hmmmm like a week or 2 ago and with In those 2 weeks when it all started i installed a nismo fpr and a hks bov i say that cause it might have something to do with it okay well first off.....
my car idels now and it never did that untill the fpr.... it stays still once the car is completly warm but if its cold it will stay at 500rpm and if i try giving it gas it will go up very slow even if i gas it hard untill it hits 2,500rpm then it will go up fast, If I decide to take off while the car its'nt completly warm , lets say im in 2nd gear in 4,000rpm and go into (N) the rpms drop quick all the way doiwn to 2-300rpm and then go back up to normal 700 but once the car is warm its okay no idel nothing .... is that normal?????? o also if i rev it right in the morning smoke comes out of my exhuast, is that normal?
Also for some wiered reasone my car didnt turn on today well i got in turned the key and there was no power at all no radio nothing, i moved the battery a bit and turned on right away, and for the past week my stereo would turn off and on, and my brake light inside is always been on but kinda turns off if i gas it hard my front turn signalls light up when i step on the brakes so yeah any help would be great!