Yes. This is all handled via udev, udisks & co., XFCE, Gnome and KDE have nothing to do with it (other than having it work more or less out of the box).
udev existed before systemd, but was merged to it sometime in 2014. By quick Googling there are still several forks that maintain it as a separate component.
My understanding is it's in the same repository (for convenience), but is logically separate, so "forking" it mainly means copying the correct directory.
Eh, not really. Many Parabola users who use OpenRC instead of systemd still use systemd-udev, as opposed to eudev or one of the other non-system forks.
I don't know what they use, but there's always eudev, Gentoo's fork which works just fine, and offers pretty much everything that udev offers (except for the systemd dependency).
I personally don't think it's that much of a trouble to just journalctl for the /dev/sdX of the inserted device and then sudo mount /dev/sdX /mnt/tmp manually, because I so rarely plug USB drives. For permanently attached or frequently used devices you can add them to fstab and mount by UUID to a fixed path.
Either way, you will still always need to umount manually or risk loosing data.
Honestly -- I have no idea, I only had to do it a few times, on Yocto and buildroot images, and in pretty restricted cases. It was pretty easy (basically udev has this file which matches a set of device selection rules with a set of actions, effectively saying "if I encounter a device of this type, I'm going to do these particular things"), but I googled my way through it.
I expect there are some distro-specific hoops to jump through, but I have no idea which ones -- I really don't like automounting, I keep it disabled even on KDE.