Это не повод спешить.

Это here works like a neutral “dummy subject” meaning this/that/it (situation). Russian often uses Это + noun to make a general evaluation:

• Это не повод... = “This is not a reason/occasion...”
  You can sometimes drop it in speech (Не повод спешить.), but Это makes it sound more complete and “sentence-like,” especially out of context.

Because the structure is basically X is Y:

• Это (есть) повод = “This is a reason/occasion.”
  Russian usually omits есть (the present tense of “to be”), so the predicate noun (повод) stays in the nominative.

Often, yes. A dash is common between Это and a predicate noun phrase for emphasis/clarity, especially in writing:

• Это — не повод спешить. (more “written,” a bit more emphatic)
  Without the dash (Это не повод спешить.) is also correct and very common, especially in everyday text.

After nouns like повод (reason/occasion/pretext), Russian very often uses an infinitive to express the action:

• повод + infinitive = “a reason to do (something)”
  So повод спешить is the natural compact pattern. A fuller alternative would be:
• Это не повод, чтобы спешить. (possible, but heavier and often less natural)

спешить is imperfective and expresses the general idea of “to be in a hurry / to hurry” as a behavior or ongoing manner. It fits well with “there’s no reason to be hurrying.”
поспешить (perfective) would mean “to hurry (and do it once / make a quick move)” and can sound more like “to rush (to act/decide)”:

• Это не повод поспешить. can work in some contexts, but it often implies a single concrete rushed action/decision.

They overlap a lot, and both can translate as “to hurry.” Common nuance:

• торопиться is very common for “being in a hurry” in everyday speech.
• спешить can sound slightly more “bookish” or like “to rush” (and it’s also used in set phrases).
  So Это не повод торопиться. is an extremely natural variant.

Это не повод... usually means “That’s not a reason/that’s no reason...” (a rejection of the justification).
If you want it stronger, Russian often uses:

• Это не повод для... (more explicit)
• Это вовсе не повод... = “This is absolutely not a reason...”
• Это никакой не повод... = “This is no reason at all...” (very emphatic)

Russian has two common patterns with повод: 1) повод + infinitive (most common for actions)

• повод спешить
  2) повод для + genitive (common for nouns/activities as things)
• повод для спешки = “a reason for haste”
  Both are correct; the infinitive version is especially idiomatic when you’re talking about what someone might do.

Yes. Word order is flexible and changes emphasis:

• Это не повод спешить. = neutral, common
• Спешить — не повод. = focuses on speshit’ as the topic (“Hurrying is not a reason/justification.”)
• Спешить не повод. = more colloquial; often said quickly in speech

They’re related but not identical:

• причина is more like a real cause/explanation (often objective).
• повод is often an occasion, pretext, or “justification to do something” (sometimes implying it’s not a deep or valid cause).
  So Это не повод спешить often carries the idea “This isn’t a good justification for rushing.”