Building image with custom kernel and DSDT

Hello.

I'm trying to build a Kali image for my Surface Pro 4, and I need to patch some kernel files to make the touch screen and the keyboard cover to work.
Do I simply need to patch, compile & install the kernel on the host on which I'm generating the image or should I do something else?

Also, I'd need to load a custom DSDT into initramfs at boot, because the Surface Pro 4 firmware is bugged and doesn't notify the OS when the power plug is connected, resulting in behaviors like the computer powering off at low battery with the power plug connected. I'm not really experienced with live system, is this even feasible? How could I achieve it?

Thank you.