I think you are being too nitpicky.
For one thing, they live in a somewhat advanced world in the Pokemon world. They have advanced technology, such as a Pokedex, a video phone which is standardized everywhere, amongst other things. If they are able to heal Pokemon quickly, why shouldn't they be able to heal humans quickly as well?
And another thing: it's quite possible that her mother didn't want to worry her, so she hid the fact that she broke her leg from her after it has happened. As a result, her mother's leg was already in the process of healing.
With regards to the "moving mouth" thing .. that's not fair. That's the style of Japanese animation. If you can say once that their mouth doesn't move, why not say other things like, "sweat drops on the back of their heads don't appear that big" or "a blast like that couldn't send team rocket flying, and even if it did, they wouldn't be able to survive when being dropped from that height. Too nitpicky, in my opinion.
Does anybody know the name of the girl? "Olyshia" sounds like a very strangely spelled and pronounced name. If anybody can verify that it's Alicia instead please let me know.
About your first point: Before Brock says Olyeshia's(or Alisha's)name the girl tells him that her friends call her "Trixie." Maybe in the Japanese version the girl had a nickname that would give away her first name (ie Tina for Christina or Jen for Jennifer). It is annoying though.
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