When sending e-mails, can others pick them up, threw a router?

Question

When i logged on the little box lower right hand corner show the
connection if it is good. it came up with someone eles name on it.

Answer 1

Then you're on someone elses' wireless line and it is not secured, it's nothing to do with email's, but the email's will be sent (if you sent any using their wireless connection) under their IP #.

All it is, is they have not secured their wireless connection and they are the ones that are open to people hacking their connection. Make sure your connection is secured.