Why iPhone 7, 8, 9, and 10 no headphone jack? Why iPhone 9 no phone? Why iPhone 10 no home button? What will Apple remove in the parts of?

What will Apple to remove in the parts of iPhone?

Losing the headphone jack allowed them to reduce costs but also improved reliability, allowed greater water resistance, and gave Apple the chance to progress to a form factor which has almost the entire front of the phone to be a screen, as seen on the iPhone X which finally lost the Home button which had always been another source of unreliability as well as hogging a wide band at the bottom front of the screen.

Bluetooth headphones are now very good indeed and there's no cable to get tangled/broken. Also no headphone socket means the phone needs no internal headphone amplifier and digital to analogue converter, although for the time being they are still fitted to permit the Lightning to headphone socket accessory to work. But Apple will likely omit those components on whatever comes after the iPhone X if they think that wireless headphones have grown sufficiently popular, and that will also save them money on manufacturing costs.

One real advantage of going wireless is that the headphones themselves will need to include a digital to analogue converter and amplifier and that allows better quality headphones to do so with far better sound quality than the cheap minimalist items currently fitted to most audio devices which have headphone sockets.

There's no iPhone 9, but there was also never an iPhone 2, 2s or 3 and no 7s either, so the numbering system was never entirely logical to start with. The 2nd model started the recent trend by being named the iPhone 3G just to show that model was compatible with 3G networks after much criticism that the original iPhone was only a 2G model. The 3G was followed by the 3Gs, and after that Apple was a bit unimaginative and just called the next one the iPhone 4. But this year marked the tenth year since the original iPhone and Apple wanted to mark that with an iPhone 10, or iPhone X as it is in Roman numerals.

Only Apple know how they'll progress with future model names, and they might not even have decided that just yet.

Apple chose to remove them in lieu of wireless options. (There's no iPhone 9 by the way)
Just the result of the naming scheme.
Most phones are going with less bezels, less buttons, more screen.
Not sure how to answer that last one.