It's all about right tool for the job. With any camera/lens/TC you can get lucky occasionally and have a dead-on focused shot. But as noted by the OP, choose the wrong combo and the hit rate goes way down.
I was using the 70-200 IS II with 2.0 TC III on my 5D mk3. Mostly aviation and birds. By itself the lens is fantastic but it does t play well with the 2x TC III. At least not for critical situations. And it's slow focusing on the 5D mk3 AND my 1Dx. Wouldn't even bother on a 5D mk2. Add low light or low contrast to the mix...well..your problems seem normal for that combo.
The TC affects your aperture along with focal length. The 70-200 f2.8 becomes a 140-400 f5.6. This is why your settings changed. I'm assuming you were in one of the auto modes if aperture, shutter and ISO changed.
Canon's AF systems work on contrast. If the focus points can't see enough contrast they will hunt. This is true even on the more advanced AF systems. Difference is the more AF points, the greater chance of getting a hit. The AF system also looks at the closest object when multiple points hit. So there is skill involved in placing the points exactly where you want. A while back there was a video from Canon that explained this very well. And after playing with the AF system to test what the rep was saying it changed the way I thought about the AF system.
If you have to get to 400mm look at the f5.6 which isn't terribly expensive. Great IQ and focuses really fast with good light. Could also look at the 100-400 but the ergonomics of the push/pull take a bit of getting used to. Also, its aperture varies with zoom which drives me nuts. Either however should increase the "hit" rate. Sell the 2x.
And then practice a lot! Even with the best gear there will be a lot of wasted shots until the skill is there to back the gear up.



