How is the MAC or HMAC secret shared with the other party for verification? I've seen people everywhere say to use a MAC or HMAC with block ciphers. I think I understand the basics, but I'm still not sure how the HMAC secret is distributed so the other party can verify that it's valid. Is the secret distributed freely like the IV (though the name suggests it is secret)? Is it part of the ciphertext? Is it sent over a secure channel like the AES key?

Also, is it safe to use the same HMAC secret for each subsequent AES encrypted message after the initial connection? Assuming all keys (other than public/private keypairs) are destroyed after the connection is closed.
It is "sent over a secure channel like the AES key".

It is "safe to use the same HMAC secret for each subsequent
AES encrypted message after the initial connection".