Please, explain this for me.

首先應該指出，2同4兩句係錯o既。
其實點解要有 to + verb 呢？呢個先係你o既問題，唔單只係 to be。要知道，動詞（除左 modal verbs 如 can / will 或者o係 present perfect 同 past perfect 等完成式外 {如 have/has/had done}）都係唔會緊接住另一個動詞。諗下ｄ簡單、大家都記得唔會錯o既句子：
I want to go to her party.
want 後如果再接動詞，要有to，呢個叫做 to infinitive（相對 modal verb 後就用 bare infinitive，即冇左to）。如果一個動詞唔足夠講你要講o既意思（如上例「想」，想做乜呢？），咁就要用 to infinitive 去補足。
你o既第一句，all our pens are manufactured 講到被製造出o黎，但未講到造成點，所以要用 to be identical... 補足。
睇第二句，All our pens are manufactured，再加 is identical 〔其實應該係 are identical〕的話，你就要諗下：
X is happy. is/am/are 後一個形容詞，就係形容 X 呢個名詞（句子o既主詞）。咁第二句o既主詞係 All our pens 定 All our pens are manufactured？當然係前者，所以話第二句錯左。
第三句其實用左一個常用句式：it is + adjective + (for + something/somebody) + to + verb。第四句除左可以引上述說明理解，仲係違反左呢個句式。