Learn Hardcore Japanese: simekiri wo mamoruno ha touzen da to omou. - I think it’s natural to meet the deadline.

を marks the direct object of a transitive verb. Here, 締め切り (deadline/closing date) is what is being “kept/observed,” and 守る is the action applied to it. So 締め切りを守る = “to meet/observe the deadline.”

Why is の used after 守る? Could I use こと instead?

の nominalizes the verb phrase, turning “to keep the deadline” into a noun-like chunk so it can be the topic: 守るのは = “as for keeping (it) …”. こと can replace の here with little change in meaning:

締め切りを守るのは当然だ
締め切りを守ることは当然だ Nuance: の is a bit more colloquial/immediate; こと sounds slightly more formal/abstract. Both are fine.

Why is は after 守るの instead of after 締め切り?

With 締め切りを守るのは, the topic is the action “keeping deadlines,” not “deadlines” themselves. If you instead want to topicalize “deadlines,” you can say:

締め切りは守るのが当然だ = “As for deadlines, keeping them is natural.” This shifts the focus from the act to the thing.

Can I use が instead of は (i.e., 締め切りを守るのが当然だ)? What’s the difference?

Yes. Rough nuance:

〜のは当然だ: topicalizing; presumes shared context and presents a general stance. Often sounds a bit more opinionated/contrastive.
〜のが当然だ: neutral subject marking; states the fact “the act of doing X is natural.” Both are acceptable; choose based on whether you want to set “doing X” up as the topic or simply identify it as the subject.

What exactly does と思う mean here, and what is と doing?

と思う means “I think (that) …”. と is the quoting particle; it marks the preceding clause as the content of your thought. So 当然だ is being quoted in your mind: “(I) think ‘it’s natural’.” The quoted clause must come right before と思う; you can’t move と elsewhere.

Why is there a だ before と思う? Can I drop it?

当然 is a na-adjective, so when it functions as a predicate before と思う, it needs だ: 当然だと思う. In careful speech and writing, keep the だ. In casual conversation some speakers omit it (e.g., 当然と思う), but many consider that sloppy; it’s safer to include だ.

Is this sentence polite or casual? How do I make it polite?

As written it’s plain/casual. Polite versions:

締め切りを守るのは当然だと思います。
More formal/businesslike: 締め切りは厳守すべきだと考えております。 or 締め切りを守るのは当然であると存じます。 (very formal)

Can I omit の or だ?

Omitting の: Not here. You need の/こと to nominalize the verb phrase before は. Without it, 締め切りを守るは is ungrammatical. You could restructure to avoid の: 締め切りは守るのが当然だ.
Omitting だ: Before と思う, keep だ with nouns/na-adjectives in standard speech: 当然だと思う.

Is 守る the right verb for “meet a deadline”? Any other options?

Yes. 締め切りを守る is the standard, natural way to say “meet/observe a deadline.” Alternatives:

締め切りを厳守する: “strictly observe the deadline” (formal/business).
締め切りに間に合わせる: “make it by the deadline” (focuses on finishing in time).
For rules/policies: 〜を遵守する is formal “to comply with/observe” (e.g., 規則を遵守する). With deadlines, 期限を遵守する appears in formal writing.

What’s the difference between 締め切り and 期限? And how do I write 締め切り?

締め切り: a closing date/time for submissions, applications, etc.
期限: a time limit or due date by which something must be done/paid. Writing: You’ll see 締め切り, 締切, and sometimes 締切り. Modern style guides often prefer 締め切り (with the り in kana). Signage and forms may use the short 締切.

What is the overall grammar pattern of this sentence?

It’s the common pattern:

[Verb-plain + の/こと] + は + [na-adjective + だ] + と + 思う Applied here: [締め切りを守る] のは [当然だ] と思う.

How do I express “should” or “must” instead of “it’s natural”?

“Should/ought to”: 締め切りは守るべきだ（と思う）.
“Have to/must”: 締め切りは守らなければならない／いけない; polite: 守らなければなりません. These are stronger than 当然だ, which frames it as an obvious expectation.

How do I negate this, and is there a difference between 〜だと思わない and 〜じゃないと思う?

Both exist, with a subtle difference in focus:

当然だと思わない: “I don’t think it is natural.” (negates the thinking)
当然じゃないと思う: “I think it isn’t natural.” (asserts the negative judgment) In everyday speech they’re often interchangeable; the second can sound a bit more assertive about the negative claim. Another careful option: 当然だとは思わない.

Do I need to say 私?

No. Japanese usually omits first-person pronouns when obvious. You can add it for clarity or contrast: 私は、締め切りを守るのは当然だと思う。 Using two は is fine here: first sets the speaker as topic, second sets the action as topic within that.

Can I change the word order?

The quoted clause must stay before と思う, but you can re-topic/reshuffle within reason:

締め切りを守るのが当然だと思う。 (uses が)
締め切りは守るのが当然だと思う。 (topicalizes deadlines)
Polite: 私は、締め切りを守るのは当然だと思います。 Avoid splitting と思う from its quoted clause.

Is there a difference between 当然 and 当たり前 here?

Both mean “natural/obvious.” Nuance:

当然: slightly more formal/neutral; good in writing and polite contexts.
当たり前: more colloquial; can sound blunter or judgmental depending on tone. So 締め切りを守るのは当たり前だと思う is fine in casual speech; in business or neutral writing, 当然だ is safer.