Is a hidden network necessary in my home? What advantages are there, if any?

I am having some difficulty in getting my home wireless network to send my e-mail. The small HP iPAQ111 recognizes the network and connects to it, but will not send any e-mails. I have wondered if part of the problem is having the network set up as a hidden network. There are very few houses near me which could connect to my network so I wonder if I need to specify that the network is hidden.

Can anyone shed some light on the two parts of this question 1-Is a hidden network necessary? and 2-Why can I not get any of my e-mails sent out? At one time everything worked, but suddenly it does not. I can erase all the settings and start from scratch if necessary. I would appreciate any good insights anyone may have.

1: A hidden network is not necessary, because your router's MAC address is broadcasted anyways, so anyone using a WiFi stumbler program could find it.

2: Not sure on that one. Is your router not allowing email ports out? Those would be ports 110 (POP), IMAP (143), SMTP (25).