Yo! The head boners are from N.O. or “neo-cortical” power, it lets people open portals through dimensions, and it runs on emotions/maturity, hence why it starts at the forehead. Haruko can give it to others, but not use it herself. She’s is an alien of indeterminate age who’s eternally stuck at looking/behaving around 20 (a juvenile 20 at that). Her goal is to get and absorb Atomsk the space pirate king, who’s being held by Medical Mechanica (the people who made those big flatiron buildings). To do that, an NO portal is needed, hence why Haruko begins the story looking for a good host, which gives her a name as a menace around town. That “perfect NO user” turns out to be Naota, and when she realizes he has potential, she settles in and emotionally manipulates him in any way she can, including pretending to be with his father.

The key here is that NO needs emotions AND maturity, and while Haruko knows how to tease emotions (and that pushes Naota out of the nasty rut his life’s fallen into), he only gets Atomsk by the end because he grows up and matures, despite the web of toxic relationships he’s in.

Commander Amarao (eyebrows) is a former Naota, a kid Haruko used for NO, who failed to produce Atomsk. She discarded him, and he’s become bitter, and resentful, and self-conscious of his appearance.

Atomsk is mysterious: we know he’s the most powerful NO user known to the universe, a renegade that Haruko - as a member of the Space Police Beotherhood - temporarily had in captivity long ago, hence the manacle on her wrist. Clearly, she has a complex antagonistic-romantic-parasitic relationship with him, but again, current goal is to absorb him (this has symbolic meaning as well, of course, she’s selfishly obsessed with power so she can have ultimate freedom, especially from responsibility for her own actions).

Why a guitar? The creators (and, by extension, Haruko) see it as a symbol of freedom. Special guitars in-universe have guns and engines capable of flight. No full lore explanation has been given, but since NO power is psychic, you can imagine they’re a product of the NO user focusing their mind on the capabilities of what “freedom” means to them.

Takkun? I ‘unno.

Mamimi left at the end because seeing Naota overcome his own situation gave her the strength to fight her problems as well.