Car does not start the first few times?

I have the vehicle listed above with a push start. My car doesn't start the first few times I push it or I have to jump it, especially in the morning, more so durn the cold months, the radio turns its self-down and if I turn it back up it just keeps going down I have to turn it up and down multiple times before it goes back up, today my car got stuck on 10 mph but the rpms when way up and I had the gas petal all the way to the floor, I had to pull over and turn the car off 3 times before it worked. The last time I had to turn the car off and open the door which makes me not have to wait for everything like the radio etc, to turn off and when I turned it back on, it took 3 tries with the push start (which has become the norm if I don't have to jump it ) before it started and went normal speeds. Also, sometime after having to jump it I get a transmission light with a! That says malfunction check owner's manual and if I turn off and back on it goes away also sometimes my car makes a loud clunky sound when I take it out of park and put into drive. As if my transmission is going to fall out. I have to jump it every morning all winter long I notice if it's warm outside I don't have to jump it or only jump it once when first using, I was told battery was good though its same battery that came with car, the clunking sound happens maybe 3 times a week I had the car inspected last month and when connected to the code machine nothing came up. I replaced the battery in my key fob twice but will get a message no key is detected every time I go to start my car. I will have to sit the FOB on top of the starter and wait a few minutes and tries before it starts if I don't have to jump it. When I jump it however it starts right up. I also noticed that I can't leave my lights on auto as if it's draining my battery but not all the time more so in the winter with temperatures 40 degrees or below or
I had a fault and had the hazards on for a while but drove an hour and a half home after fixing flat and my car battery still didn't recharge though I don't know if there's a dead spot in push start, something electrical, I can't find a mechanic who has actually looked at it and has an answer for me.