engine problem

I have a 2004 rx8 I have two questions.....question 1 under heavy acceleration at about 4 rpm my car seems to miss fire and check engine light comes on then goes away car runs fine until I hammer the gas and then same thing any idea's? ?.....question 2 if I don't start the car at least once a day my battery goes dead what is draining the battery? I have replaced battery 2 times in last six months i have a battery tender on it but if i leave it off for a day or so the battery is dead thanks for any help