My 99 Ford Taurus, Fuel pump, fuel injectors fuel filter? Having trouble starting

I bought a used 99 Ford Taurus about 6 months ago. First is just didn’t start smoothly. But it started. I was never worried that it wasn’t going to start, I could just tell the difference. Then one cold day a few weeks ago, my car turned over but didn’t start. I was low on gas about a quarter or less. It sat over night. I tried starting it a bunch of times and it would just turn over. 20 minutes to an hour later, I tried a bunch of times again, turning over and over and it started. It would start fine for the rest of the day. I noticed when my car was low on fuel it struggled the most, so i tried to keep my fuel tank over half, that helped, but I realized every time it happened, the fuel had to be a little bit higher each time. And it was always after the car sat for a while, if it started once for the day, it usually always started for the rest of that day. Then a few days ago, I parked down hill. My gas tank was full so it was like " over full". It started that day but a few hours later after sitting down hill, when I went to start it, it did something different. It was like there was almost too much gas, it was struggling to start too, but differently, almost like gurgling the gas if that makes sense. It eventually started. Now starting a day or two ago, even with a full gas tank, its just starting but shutting off. More than turning over but not completely turning on. (If I hold the key, its like as if i have it started but its choking.) I press the gas sometimes in all these situations. I try over and over again and eventually it starts. So before I take it to an mechanic (which I just did. I got the upper radiator hose, ford engine hose, bypass hose and hose clamps all replaced) what could it be? I read about fuel injectors, fuel filter, fuel pump. Is there anything else I can be aware of? Or understand better? Any advice please is much appreciated. If you need more info please ask.

Oh, also no CEL on, I took it to autozone and the guy said my battery was fine, but my alternators levels are off, theyre 6 I think, 4-6, but theyre supposed to be at 12? 12-15 I think he said, I’m not sure.

Could be the fuel (and pressure) are draining back to the gas tank. Try this: turn the key from Off to Run (not all the way to Start.) If it’s quiet you may hear the fuel pump run for a couple seconds - that’s a good thing. Turn the key back to Off, then Run and give it a couple seconds for the pump to run again. Each time it’s turned from Off to Run the fuel pump will bring fuel and fuel pressure up to the engine. After doing this “key dance” 2-4 times, turn the key all the way to Start. If it starts, great.

If your alternator is not charging the battery that is a different problem, not directly related to the hard starting unless and until the battery can’t even turn over the engine.