If I change a .mk or a .xml file in the android source code, how do I send this updated file to the device? Do I first rebuild the source tree? Or is building not necessary? After building/not-building, do I use adb push or adb sync or do I have to reflash the device?
No you can't just push the these files as these files are merged in the img file like boot.img ,system.img etc. so you need to find out that in which img file these .xml files are added. Then you just need to make that img file like
make bootimage -j4
and flash the image to the device
In case you did't figure out then you need to rebuild the source tree.