Which filesystem does Android attach to the root directory? I know that Android uses FAT32 for SD cards and mounts them via FUSE. But which FS is attached at /? Some kind of ext? ZFS?
There is no singularly defined "Android" filesystem, so this can vary between devices.  Any FS that the kernel can load drivers for is basically fair game.

By and large, you'll almost certainly find that ext4 is the most common filesystem on modern devices. Older devices may use older ext* versions as well, or other filesystems entirely. Since everything is built on Linux, ext4 a pretty sensible choice, with solid kernel support and a good track record. You can read a bit about why this decision was made in Ars Technica's article about the switch to ext4.

Some devices have also used Samsung's Flash-Friendly File System (f2fs). Notably, several of Motorola's devices, as well as the Nexus 9, use f2fs. The goal of f2fs was to create a file system that was designed specifically with the needs of flash-based storage mediums in mind, in an attempt to maximize performance on devices using NAND chips for their primary storage medium.

This does not mean that these are the only filesystems that Android is capable of running on, however, as I noted above. Given the kernel source and the know-how, it would certainly be possible to include drivers for other filesystems in a kernel image. Android x86 supports installation on NTFS and FAT32 filesystems, for example.