1. A newly graduated cryptologist recommends encrypting the first 80 bits of the message with a secret key (known only to the sender and receiver) and using those 80 bits as a signature, thus saving time compared to standard signature techniques. What's wrong with this thought?
2. This time, the same cryptologist is tasked with developing a method to prevent the modification of messages from outside (intruders). Our expert offers to add the hash of that message to each post. Why does this method not solve this problem?

Note: The hash function used is a powerful hash function.