I do not know the address from which I sent you the money (when I click in Bitcoin-Qt ''Transactions'' then ''Transaction details'' it doesn't tell me which of my public addresses was used for making the payment in your favour) so I cannot enter my public address by myself (am I correct or not?)
This is a good question, and I don't know the answer -- little help from someone with more expertise?
2. Are you the only person who can see my message?
The answer to this question depends on how the message is transmitted, but it should be assumed that anybody can/will see the message, which is why it is recommended that the content of the message contain the specific details of the context of the message, e.g. "This message sent on this date to so-and-so is for this purpose..." This will prevent the message from being hijacked for other purposes.
1. Blockexplorer?
2. A signature is only a number that proves that a certain message was approved by a certain address