If a woman writes a message to a man (in a dating context, I presume), and begins with the address "Hey sure,", what does this mean?

no idea! I don't think it means much, though. what is the context of the email?

The context is basic correspondence about meeting up, spending some time, I suppose. Just to clarify, the address is "Hey Sure..." in the sense that she's calling him Sure (not the adjective, that is).

It probably means that English is her second language.

ha! good one, Marea.