The lag time between ePals accounts is usually very small. (30sec) For emails outside of ePals it depends on a lot of different things. If it is a peak time, (in the mornings or right after school is out) it could be up to 10 minutes on a really busy day.
There are a couple of reasons your gmail account didn't work also.
If you are sending to a Global Community student user, it will not go through. They can only send and receive emails from the ePals community.
If you are sending to a SchoolMail student user, it depends on what access level the school administrator has set. It could be as narrow as the student can only send to members of their class, school, or district. Or it could be opened to the ePals community or any email. That is what is so good about the SchoolMail setup. Administrators can give students different access levels depending on school policy or age.