what is a surname
It refers to your family name (in patriarchal societies the name you get from your father). In many western countries it is also termed your "last" name (because of the order in which names are usually written). In many Spanish speaking countries (at least when being formal) it's the next-to-last (followed by your mother's family name).
In many Asian countries the family name is normally written/said first (followed by the given name(s)).
The most cultural-independent term is "family name". For the same reason it may be better to refer to your "given", rather than "first" or "Christian" name.
Yes the familey name as I answered you in comments on your previous post.
A surname is a person's last name, for instance, Riley. Or Gonzales. Etc.