공감 means empathizing or feeling the same.

나도요 / 저도요 means "me too" Use 나 for "I" less formally, like with friends. Use 저 for "I" formally, speaking to stranger or someone older. You can drop 요 ending if you are on close terms

it depends on the situation but normally we use 나도 같은 생각이다, 동감이다