Too/so/either/neither

Are all of the following conversations correct?

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A: I like ice cream.

B: Me, too. or I do, too. or So do I.

A: I can play the piano.

B: Me, too. or I can, too. or So can I.

A: I am hungry.

B: Me, too. or I am, too. or So am I.

A: I don't like hamburgers.

B: Me, either. or Neither do I. or I don't either.

A: I can't cook.

B: Me, either. or Neither can I. or I can't either.

A: I'm not tired.

B: Me either. or Neither am I. or I'm not either.

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Would you be so kind as to help me?
Thanks!

PS I also posted the same question on https://www.usingenglish.com/forum/threads/253581-too-so-either-neither?p=1345143#post1345143, but all of your answers are unique to me. Hope we can discuss with each other. Thank you.