I'm afraid the embassy won't accept visa application by mail. If you can't go to the embassy in person, you may entrust anyone to do it at you own discretion. But you have to complete and sign the Visa Application Form yourself.
Generally, the validity of a single-entry visa is 3 months, counting from the day of application. So please make sure you are going to use it before it expires.
The round-way air tickets may be required.