How can I know which file system is used for my internal storage? I want to know whether my internal storage is formatted as exFAT, FAT32, ext4, etc.

How can I tell?

I run rooted Android 5.0, if it matters.
For this you need either access via adb (adb shell) or a terminal app. At the prompt, execute

mount | grep "/data"


The output will have something like

/emmc@usrdata /data ext4 rw,nosuid,nodev,noatime,discard,noauto_da_alloc,data=ordered 0 0


The third column tells you the file system used (in the example above: ext4).

Of course there are also several 3rd party apps offering you such insight :)