The FDR-AX100 has face tracking focusing but it only works if white balance is set to auto AND one of aperture, shutter speed, or gain is set to auto.

Worse, it does not always tell you why face tracking is disable. If you put white balance in outdoor mode, it would tell you. If you put white balance in other modes that is not auto, it would not tell you; it just refuse to work. It's almost like it doesn't want you to use this feature.

Are all sony camcorders/cameras like this? I was considering AX700 but not if it has the same face tracking limitations.

I have an old canon HF G10 and it faithfully does face tracking regardless of white balance and exposure settings. Would it be fair to say Canon has better face tracking than sony?

Actually I want to ask owners of AX700, can you test if face detection works if white balance is NOT auto?
How about if exposure settings (aperture, shutter speed, gain) are all set to manual?

Check out the Sony Help Guide available on-line. In the Help Guide (October 2017) on pages 46 > 63 it covers focusing, then pages 62 and 63 covers Face Detection. There is a lot of information covered on these pages

Also, pages 166 > 168 covers the FOCUS AREA. Within those pages it covers Phase detection AF. There are some limitations mentioned but I didn’t see the ones that were your concern.
- [FOCUS AREA] setting is not enabled when using a zoom other than optical zoom and the focus frames re displayed as a dotted line.
- Focus area setting is not available in Super Slow Motion recording.

Lots of reading material so hopefully some answers to your questions.
[edit: didn't see your post #2. Don't have time to answer #2, too much other stuff to do!]

Are all sony camcorders/cameras like this?

Absolutely not. Frankly, I'm skeptical that the AX100 has the limitations that you have described. It makes no sense to design a camera where WB has anything whatsover to do with focus. I don't have an AX100 to test myself, so I cannot say for sure one way or the other, but the operation manual makes no mention of such limitations. I think you are incorrect.

Actually I want to ask owners of AX700, can you test if face detection works if white balance is NOT auto?
How about if exposure settings (aperture, shutter speed, gain) are all set to manual?

Face Detect on the AX700, NX80, and Z90 is not affected by white balance or exposure settings.

Absolutely not. Frankly, I'm skeptical that the AX100 has the limitations that you have described. It makes no sense to design a camera where WB has anything whatsover to do with focus. I don't have an AX100 to test myself, so I cannot say for sure one way or the other, but the operation manual makes no mention of such limitations. I think you are incorrect.

The AX100 manual makes no mention of this limitation is exactly why I'm asking owners of AX700 to test this feature. Because I cannot rely on sony's AX700 manual to tell if this limitation exist.

You can check this youtube video where one AX53 owner also complains about face tracking doesn't work when white balance is fixed.
White Balance & Face Detection Limitation - Sony FDR-AX53 - YouTube
Tell him he is wrong because it doesn't make sense.

As I said before, I have never used an AX53 so I can't say if you and the guy in the video are correct or not. Maybe not, but I'm still skeptical there aren't other settings that are cassing the problem. But that is just a guess and I do not know for sure. There is no question the AX53 is a consumer camera that is not intended for professional use, so anything is possible.

But to answer your real question, and as already said yesterday, the AX700 does not suffer from this limitation.