So everything looks like it's correctly configured. I don't suppose you have access to the cron logs?
Moodle uses a scheduled task to make the connection to your IMAP server, to fetch the mail, process it, and post it. If there's a problem retrieving the message, then you will see it in the cron logs. Sadly we don't (yet) have a way of storing these automatically in Moodle, and you will need to setup your own cron logging if you don't have it already.
Hopefully this should give an idea as to what's going wrong and where.
Incidentally, the mail checker will only fetch messages from the inbox, which have not been read, and have not been flagged/starred. The act of reading the messages in your mail client will mean that they are not picked up by the mail fetcher. This is something that you may encounter during testing and should be aware of.
The reason that Moodle asks you to remove the original message when replying is because it doesn't (yet) remove the original content. There is an issue open to do this, but it's extremely hard to get right - I could go into detail if you like, but suffice to say that Apple and Google have closed patents on how they do this for a reason.
Let me know what your cron output looks like and we can continue the diagnosis from there.