Car will not turn over

Okay, so this car is giving me some issues. About six months ago, the car would shut off when coming to a stop occasionally. Does not happen every time. I put it in park and crank it back up with no problems.

Well since a few days ago, I have not had this problem, but instead when I turn the car off, it will not crank on its on. You have to boost it off. Since the battery is in the trunk and the fob does not work, I could not access the battery so I went under the hood and boosted it from the hot post located at the fuse box. It fires back up and I let it run for an hour or two. I turn the car off and again, it will not turn over. Battery seems drained. So my jumper cables have a alternator tester built in and the light glows red as if it is a bad alternator but I actually got it tested a couple weeks ago and it checked out fine and also, if it Is an alternator would the car not quit running while driving since the alternator cannot charge the battery? How could it sit and idle or be driven within stalling?

Also I would like to mention that when the car acts like it is going to stall when coming to a stop, the radio volume will get loud, without indication from the display. The radio is not equipped with auto volume

I have replaced the fuel filter and fuel pump. That is it.