Cooper39

So last weekend I purchased my first Mazda RX8 (yay!) I had been driving each day since I got it and ive been loving everything about it. today omw to class i got a CEL when i turned my car back on from getting something to eat. The error code I received from autozone was p2004 and p2005. The car randomly died on me getting home a couple days ago but came right back on. At autozone me, and the guy helping me, noticed that the battery was pretty corroded on the positive terminal and the battery passed on everything. So now today after reading around the forums and seeing that revving the engine hard could possibly solve my p2004 problem, I went out for a drive and sitting at a red light the car just randomly died again. It came right back on but did the exact same thing as it did a few days ago. Also while I was on my drive, shifting into 2nd gear the car had a hard time going into second gear like it was going to stall (like what a misfire is i believe) and then the CEL went from being solid to flashing for a few seconds but then back to solid again. The car looked really clean at the dealership and drove very cleanly up until this point. please if anyone has any info they can give me to point me in the right direction it would be greatly appreciated! Also wanted to note that I did opt for the factory warranty option when purchasing the car.