CM does not provide a way of determining paying from non-paying members.
That being said, in regards to messages:
The same way you would receive notification in your registered email address that a message arrived in your CM account, a non-paying member would receive the same basic info. They would NOT though be able to read the contents of the message until they pay to become a member.
That message will be in their account as long as the account exists on CM (paying or non-paying) just like it is on a paying members account.
Non-paying members can ONLY send emotigrams - not messages, and they CANNOT include a message in the emotigram.
Hope that answers most of your questions.
If a question remains of WHY their is no way of determining if a member is paying or not, that one has been beaten to death here in the forums (a keyword search for "non paying" shows 187 posts - not including the variations on the keywords)