You can interpret every single BRS sequence (minus the first fight) - or the last part, when B★RS breaks the chains and gives the Cool Down Hug - as a flash forward to after Mato found the cellphone charm at the very end.
The checked patterns in the Otherworld might be a reference to the checkered walls outside Mato's school, or the checkered wall next to the hill or the checkered pattern in Mato's house, etc.. The constantly recurring ★ motif is a reference to all the stars Mato has in her room and on her clothes. In short, all the Otherworld battles can be interpreted as a Battle in the Center of the Mind. Or maybe their school is the Tartarus.
In the TV series, the direct effects of the real world on the Otherworld are more noticeable. Easier details to miss include the swarm of spiders appearing in Kagari's world after she gets a kick out of a nature documentary. Showing a dog eaten by ants.
From the 2012 anime: Yuu-as-Strength's line: "You're not running away from your problems. But who is?" The line just sounds like part of Yuu's insane rants, but in fact, she's referring to herself - a girl who, rather than simply trying to help others with their own problems and shouldering hers, ran away from the real world to isolate herself in the Otherworld.
The lyrics of the theme song in the 2012 anime refer to the Otherselves assigned to the characters: "How much longer should I continue shouting?", which are Mato's attempts to become friends with people. "How much longer must I continue crying?" refers to Yomi's crippling loneliness. "No more, I can't run anymore." is what Kagari ultimately needs to do; she can't just run away from the world anymore. "The world of dreams that I once saw is shutting down." reflects Saya's attempts to stop B★RS's rampage and Strength's plight at being in the real world.
The "other selves" exist for the purpose of taking your pain for you physically so that you won't feel it other than psychologically. Yeah, every time you feel heartbreak, someone in the Otherworld is taking all that for you.
So in an alternate universe, your highschool crush beat the shit out of you. Kinky!
If other selves are awakened when a girl's psychological suffering reaches critical levels, and Saya has been purposely pushing guilt onto the girls for their traumas, consider the scene in Episode 3 where Black★Gold Saw A.K.A. Saya is seen 'gardening' what look like immature other selves. The one that looks like Kohata steps out from the crowd in correspondence to the scene where Saya is trying to make Kohata feel miserable about the love letter. If B★GS is able to create other selves through Saya's interactions in the real world, consider how many of those otherselves she tends to in the otherworld. As a councilor, this means Saya is in the perfect position to traumatize every girl in the school. It just so happens that no one in the school has greater pains than Mato, Yomi or Kagari, but she was close to awakening Kohata's other self.
In the TV series, one considers how badly it could have gone. Looking back at all of Mato's interactions with Yuu; since nobody can see Yuu; she would have been considered a very strange girl and ostracized. Look back at all the scenes of them being silly; and we'll see people staring at a girl talking to herself. Fortunately, this didn't bother her; and her situation at the end of the series turned out differently.
In addition, who knows how many girls that B★GS Saya has been sending against B★RS/Mato before this? She screws up their heads, creates an Otherself; sics it on B★RS who kills it (and likely kills Mato's memory of any unpleasantness). Mato's High School years must have been filled with girls freaking out at her; then the next day nobody remembers anything. Saya justified it in feeling that the erasure was ultimately cleansing for the girls.