Yes, you can. I currently only use them wired because I always forget to charge them. I have the whole system on a power rail which is switched off overnight. The mouse ran into an empty battery too often. Now it is permanently connected to the cable.
Yes, the mouse is Windows 11 compatible. Official ASUS support pages explicitly offer drivers and tools for Windows 11 64-bit, and firmware updates require Windows 10 (1903 or later) or Windows 11.
Found it, you can store 4 different DPI profiles that you can easily alternate with the top button. You can set up any of the mouse buttons to activate the sniper mode which basically changes the DPIs while pressed to the DPI profile number 1. So you just set up profile number 1 with the lower dpi for this mode and have one of the other profiles to be with whatever DPI value you wish for normal use.