這個(gè)句子不對(duì), 不僅僅是everyone前面加不加and的問(wèn)題,還有語(yǔ)序及結(jié)構(gòu)錯(cuò)誤.

we must know 后跟的是賓語(yǔ)從句, 賓從中應(yīng)用陳述語(yǔ)序,
而what should we done是疑問(wèn)語(yǔ)序.所以錯(cuò)了.

另外, should worked 也是錯(cuò)的, 情態(tài)動(dòng)詞后應(yīng)跟動(dòng)詞原形.

改正后的句子為:
we must know what we should do,and everyone should work hard.
句意:我們必須知道我們應(yīng)當(dāng)做什么,而且大家應(yīng)該努力工作.

Everyone should do something he like. 這個(gè)句子中的 like應(yīng)改為 likes,因?yàn)橹髡Z(yǔ)he為單三.

Everyone should do something he likes.