XT-3 Owner

Long story short: I had utterly blown out skies and reading about how to avoid them quickly led me to ND filters and all that kind of complicated stuff. Then I played with d range and d range priority mode of the x-t3. The latter gave me excellent results. If you shoot landscape and things with skies you have to try it if you havent already. Its incredible.

The only way -to my knowledge- to prevent the camera to go to My Menu every time you enter the menu button, is to leave the My Menu completely empty. The purpose of My Menu is to have quick access to the most used menu items, hence it always starts there. Should  you decide not to use the My Menu, you can always add 4 most used feature to the Q-menu and activate them with the Q-button and the touch interface of that menu.
From what you describe the 18-55 can do a couple of things in the background. When PRE-AF is ON, the camera will always focus. It could be that it still does when in replay mode (I haven't checked it as I don't have that lens). Another (more likely) noise could be that of the OIS. On the 18-55 there's a switch for that. Try it in OFF mode and see whether the noise persists.
The focus peaking for manual focus indeed needs an upgrade. I also have experience with an A7RIV and an SL2 and they have better focus peaking esp. during magnification. Esp. the A7RIV with the Loxia lenses works brilliant. The issue with Fuji is that indeed when magnifying the peaking gives a very flickery image. So either quiet it down of switch FP off when magnification is activated. Another issue is that for some Fuji cameras (e.g. my beloved X-Pro2) the focus peaking color yellow is not available for some inexplicable reason. Yellow is for most shooting situations the most visible color (at least in my experience).
Another issue is that for many menu settings there's no help function or explanation in the menu. After many years of Fuji I know most settings by heart, but it took me a while. It would be easy to have a line of text explaining the menu setting at hand. Most other cameras have such a feature. Fuji only does this for certain settings like film simulations, but consistent use would improve the usability.
Finally, some menu options are named differently on the various Fuji cameras. On the X-Pro2 there's the option "preview pic. effect" which is called "natural live view" on the X-H1. Those things can be easily aligned, even though there could be a small tech. difference between the two options. Other than that I think the Fuji menus are quite good and at least a lot clearer than the older Sony menus (not the A7SIII) but not as good as the Leica and Canon menus. It sits nicely in between 😉