Question about Message Authentication Code (MAC)

Can a MAC detect if someone altered or replace a message? Also, can someone delete a message?

A MAC can detect tampering, assuming it's a strong MAC (like SHA1), and assuming you use it correctly.
Frankly, it's the second part that is most likely to stymy you. It's easy to get strong algorithms; using them well is much, much more difficult.
A MAC is absolutely useless for detecting if a message has been deleted. In fact, detecting missing messages is an intractible problem. You can increase the odds of noticing a missing message, but you can never guarantee it.

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