How can I know which file system is used for my internal storage?

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 :)