Learn Hardcore Japanese: watasi no iken de ha, ryou no doa wo naosu hituyou ga arimasu. - In my opinion, the dormitory door needs to be repaired.

Here 私の means “my” and 意見 means “opinion.” The particle で marks the basis or context (“in/regarding”), and は turns that into the topic (“as for”). Together 私の意見では literally means “as for my opinion,” i.e. “in my opinion.”

What is the function of の in 私の意見 and 寮のドア?

The particle の links two nouns in a possessive or attributive way.

私の意見 = “my opinion” (私 owns 意見)
寮のドア = “dorm’s door” (the door belonging to the dorm)

Why is 直す placed before 必要 in 直す必要があります?

In Japanese, verbs or clauses that modify a noun always come before that noun. Here 直す (“to fix”) modifies 必要 (“necessity”), so you get “the necessity of fixing” → 直す必要.

What is the grammatical role of が in 必要がある?

必要 is a noun meaning “necessity,” and ある is the existential verb “to exist.” The particle が marks 必要 as the subject of ある, so literally “a necessity exists.”

Why do we have both を (in ドアを直す) and が (in 必要がある) in the same sentence?

They mark different relationships:

ドアを直す: を marks ドア as the direct object of the verb 直す (“fix the door”).
必要がある: が marks 必要 as the subject of ある (“there is a necessity”).

Why is the main verb at the end あります and not 直します?

The core of the sentence is “there is a necessity” (必要がある). So the polite form あります is the main verb. The action 直す is inside a relative clause modifying 必要, not the main predicate.

Could I use a different expression like 直さなければならない or 直すべきだ instead of 直す必要があります?

Yes. All three express “need to fix,” but with slight nuance differences:

直さなければならない (直さなきゃならない) is a strong, somewhat formal obligation.
直すべきだ is a bit more like stating a clear duty or recommendation.
直す必要があります is neutral and simply states “there is a need to fix.” Choose based on formality and strength of obligation.