hi i can help you , have friend track and clean all the grounds coming from the battery , they have been trouble before, here is some info on it.
Yesterday, my wife is driving the car and stops for coffee and when she returns to the car, it won't crank. No click, no nothing. Had it towed to a friends shop where he charged the battery and it started
i'm sorry i was adressing the first trouble you had ,
ok now fir the second trouble , the maf sensor is a very common cause of the miss and backfire heres a test for you.
ASE Certified Technician
ASE MASTER TECHNICIAN,30 YRS EXPERIENCE