I'm not in any way defending this – it was a mess –but wanted to answer a few things:
because she knew a bit about chemistry, she knew about the drug to sedate him, because of the dog No, she was just able to steal the sedative drug from the vet (although it does seem unlikely that someone would be left alone in a room full of drugs for long enough to swipe them!).
Sooo, the dog, who appears healthy, goes to a vet, why? what for? I agree with the PP; he was probably being neutered.
So, she knows the chemical components to recreate the anasthetic No, as before, she nicked the drug from the vet's.
how the hell did the build the thing she kept him in??? Again, as a PP says, there was a scene where she went to a huge furniture/building store and bought it.
The boy getting beaten up and his dog being left in a bag in her house in the first place
was a creaky-as-fuck plot device to get her a dog so she had to take it to the vet's so she could steal the drugs.
It was a shambles.
Tom Hughes is pretty, though, isn't he?