这好像不是英语方面的问题，总不能不知道邮件和电子邮件都是啥吧

mail 信/邮件
email 电子邮件
第一句是让你寄原件给他
第二句是复印件/电子扫描件不算官方文件
3是可以让学校发官方邮件 电子版纸质版都可以
盲猜你在申请学校一类的

A notarized hard-copy sent directly from the applicant, via mail or courier (Examples of people who may be able to notarize documents: Bank, Lawyer, Notary Public, Paralegal, Real Estate Office, Embassy)
An E-Mailed copy from the applicant that can be verified online.
An original from the applicant (if you wish for your original documents be returned, please provide a postage paid courier envelope so documents can be sent back and tracked).
An E-Mailed or Mailed copy from the institution.

第一句和第二句在意思上有什么区别。
A notarized hard-copy sent directly from the applicant, via mail or courier (Examples of people who may be able to notarize documents: Bank, Lawyer, Notary Public, Paralegal, Real Estate Office, Embassy)申请人直接通过邮局或快递公司寄出的经过公证的纸质版文件
Please note: A photocopy or E-Mailed copy of a notarized document is not sufficient and is still considered unofficial.（上述）公证件的复印件或电子邮件版均视为无效
第一句的mail和传统的email有什么不同：mail又称snail mail，即通过邮局或快递传送的纸质信函、文件，而email就是我们现在都熟悉的电子邮件
第三句的E-Mailed 和 Mailed有什么区别：参考上题。

没啥毛病