Only if you consider www.mail2web untrusted...
When it comes to passwords, the only trusted party I know is myself. Your security-consciousness may vary.
I forgot about the username format for some mailboxes, and I'm unfamiliar with what information they might require for an account anyway. The last time I heard about this type of service, I was still working for Earthlink, where, given a username and our domain name, it was obvious what someone's e-mail address was.
Only if efficiency is of no concern.
I bet I can check mail via telnet faster than you can load and log into a webmail service.
The benefit of debugging problems by talking directly to the server is that you see what the exact server response is, you don't get the mangled or "friendly" error messages that some mail clients return upon encountering an error.
If you want useful replies, ask smart questions.