1) what does "spring" mean in "you're not springing it on me as a pet"?
"You're not giving a pet to me all of a sudden (suddenly) with little or no warning"
2) What does "threshold" mean in "She eyed me from across the threshold"?
"She eyed me from across the doorway/entrance"
3) Does "Let me get your mother" mean "Let me ask you mother to come here"?
It means "Let me go and find your mother and bring her here"
4) What does "charge" mean in "I gave her a quick wave and charge inside"?
"I gave her a quick wave and rushed inside"
5) What does "the girl is working you too hard" mean?
Meaning here can vary a lot .... it depends on context.
The girl may be trying to become a friend, but is trying too hard and it's becoming irritating.
Or in a work situation where the girl is assigning work, she is giving you far too much work so that you are working way too hard.