Allow anonymous users to subscribe to newsletter/mailing list
Sounds like your site can not send e-mails for whatever reason.

The default newsletter settings require to confirm a subscription, you can disable that in the newsletter settings, optionally also only for testing until you've figured the e-mail problem out.

Unconfirmed subscriptions aren't displayed in the UI, that's why you can't see anything.

Instructions on how to use and configure Simplenews can be found in the README.txt and the online documentation.

Note: You're asking a lot of different questions, and your actual problem (sending e-mails being broken) has nothing to do with initial question (you might not have known that, so that's ok). Remember that you're supposed to accept a (single) answer as the correct one, how can you do that if you ask multiple, different questions?