2010 Nissan Altima Starts, but Dies when taken out of Park

Every time I start the car, it starts right up no problem. It doesn't make any
weird sounds or rev or anything. The second the car actually clicks out of park
it instantly dies. I can get it in reverse, neutral, or drive, but it dies every time.

I don't know if these problems have anything to do with the car dying, but... Ever since I got the car, it does take about 3 seconds for the car to realize that
I have taken it out of park and put it in drive or reverse. It also stutters
sometimes when it goes from stop to go, but only a little bit. And when it
comes to a stop, it drops into 1st gear way too early and the car stutters as
well.

Any help would be greatly appreciated. Thank you.