Can I say,"My favourite animal is dolphin."?
Does it sound smooth to native speaker's ?My main uncertainty here is the form of the word dolphin.Since native speakers give me different answers on this issue,to wit,should it be dolphins,dolphin,or the dolphin.Thanks for answering.

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Mostly, I would say "My favorite animal is a dolphin."

You could also say:

"Dolphins are my favorite animal"
"My favorite animals are dolphins"

Any of these will sound natural to native speakers, especially when spoken. We don't care too much, in conversation, about whether or not dolphin is plural.

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I believe there's also a species of fish called a 'dolphin' in English. I think it's a Pacific species.

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Dolphins are my favorite animal too!

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Well I completely agree with Steven. Nothing more to add :)