Yea, well. (Not having seen the movie yet) the way I see the song is
The verses are "broken girl" dealing with her life (Sakura's had a fucked life) and unfamiliar feelings (@ Shirou, her one light).
The first two refrains are Sakura's nightmares/lolEvil whereas the final refrain/ending is her screaming through after she gives in to lolEvil.
"mud" is also what spills out of the Grail in the ending of Zero.
At least that's what was used in the VNs translation that I saw. Not sure if it's the same word in Japanese.
Kirei infodump from Heaven's Feel (possibly to be adapted in the 3rd movie).
If you only watch the first sentence (50m12s) and have seen Zero it's nothing too bad. Hard spoilers for pretty much EveryThing in this video otherwise.