Repeating nonce in CTR mode Can anybody explain in detail why repeating nonce is dangerous in CTR mode?

Two cases to explain


When plain text is repeated for each nonce.
When plain text is unique for each nonce


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In counter mode the block cipher operates as a PRNG, essentially like the keystream generator of a synchronous stream cipher. The key and the nonce determines the starting-point of the PRNG, thus if the nonce is ever reused with the same key, the keystream produced is the same.

Why is this bad? Because if you ever figure out the plaintext corresponding to the ciphertext of one message encrypted with the repeating keystream, deducing the keystream is trivial ( ciphertext = plaintext XOR keystream ), and you may easily decrypt any other message encrypted with the same keystream. (Essentially a known-plaintext attack).

To answer your specific questions:


If the same plaintext is encrypted with the same nonce (and the same key), the ciphertext is identical.
If the plaintext is "unique" (different is perhaps more accurate), the ciphertext is different. But as explained above, if the adversary gains knowledge of any plaintext-ciphertext pair, (s)he may decrypt all the other messages.