Because of what Ash said about the perfume at the beginning, and the Girl Scouts at the Gym overheard him, so they probably told Erika not to battle him.
It was kind of implied her assistants were obnoxious fangirls and aggressive to all who opposed Erika by their own accord. From what I remember there was nothing suggesting Erika actually gave the order to ban Ash herself. She only turned a blind eye to them violently throwing him out her store (though you could blame his friends for being as ignorant towards that action, no one really contradicted slapstick assault in Kanto ).
I haven't watched any of the Sun/Moon anime (in fact, I haven't watched the anime since the XYZ series), but from reading about it on Bulbapedia, I think Tapu Fini actually showed Mallow an illusion of her mother with its magical mist. In her place, a rose grew, which turned out to be Shaymin, so it's more than likely that Mallow's Shaymin is her mother reincarnated as a Pokémon. Which makes me wonder if other humans in the Pokémon world can be reincarnated as Pokémon when they die.
(By the way, was it ever specified what Mallow's mother died of? They say she was very ill before she died, but they never really said exactly what illness she had.)
Yeah I don't think they were on-the-nose about what killed her, just she was sick.
From what I remember her spirit also gave a contemplating look just as she had to leave, either knowing she had to go or deciding she had to think up some sort of backup plan, thus became Shaymin.