Ford Tuarus - are multiple problems related?

I have a 2001 Ford Taurus SES. It has been running fine for the last two years.

2 months ago, the engine light went on and the mechanic replaced the coil.

1 month ago, the car started running very rough and the engine light started flashing. The mechanic replaced three fuel injectors.

Now, it's having trouble turning over. The first time I try it, it sputters as if I left the lights on. The next time I try usually it turns over. The same mechanic said it was the battery and/or the starter. I called AAA, since the battery was under warranty. AAA said it was fine - 680 cA, so it must be the starter.

Questions:
1) I'm not a car guy, but do repair cameras, and know that one thing changed can effect another. Are all these things related?
2) Is it possible the mechanic diagnosing the wrong root problem, which is causing these things. It was definitely bizarre to me that the mechanic said the battery was 300cA, but AAA said it was 600cA.
3) Is there anything I should try in order to get the car to turn over properly, outside of replacing the starter?

I keep sinking money into this car.

Thanks,

Kevin

If there's a loose or dirty connection that could explain the differences in CCA readings as well as the intermittent issues you are experiencing. I'd start by disconnecting the cables at the battery and making sure they are clean and in good shape. If so, reattach and make sure they are tight on the battery posts. If you're ambitious, you could pull the battery tray and make sure there isn't corrosion in the cable below the battery tray. That was a common problem on some model years, although I thought they resolved that in 1999.

-Rod