Does "get me" always mean "buy" in a context like the following:
Get me some batteries, please.
Can a teacher say to a student Get me a piece of chalk (from another classroom).
If I were a native speaker of English, I would never shut up. :-)
You haven't provided any context, just one sentence.
"Get me" doesn't mean to buy. It can, but it doesn't have to.
"I'm going to the store."
"Get me some batteries, please."
In that context it means to buy. In a different context, it means to go fetch.
"Honey, get me some batteries from the closet next time you're up."
Yes, a teacher can say that to a student, though "Go get me..." would be more common.
Unless you are doing some book English exercises, the combination 'a piece of chalk' would sound really awkward to me if I heard that in a real conversation or informal writing (like an Internet blog). Though I could imagine somebody say 'Go get me a chalk' or 'Go get me some chalk'.
Can you guys please comment on that?
P.S. I'm sorry if I'm hijacking this thread.
Both "..a piece of chalk" and "...some chalk" sound natural to me. "A chalk" does not.
I wouldn't say "a chalk." I would say "a piece of" or "some."