Нам стоит устроить небольшой перерывчик и немного погулять в парке.

Because Нам стоит… is an impersonal-style construction meaning something like It would be good for us to… / We should…

• Нам is dative plural (to/for us).
• The “doer” isn’t the grammatical subject here; instead, Russian marks the person who benefits/should act with the dative.

Стоит has several meanings, but here it means it’s worth (doing) / one should (do).
Common patterns:

• (Кому) стоит + infinitive = (someone) should / it’s worth (someone) doing
  So Нам стоит устроить… = We should arrange… / It’d be a good idea for us to arrange…

It’s usually softer and more like a suggestion. Rough scale (often):

• нам надо / нам нужно = we have to / we need to (stronger)
• нам стоит = we should / it’d be worth (advisable, recommended)
• можно = we can / it’s possible (permission/option)

After стоит, Russian uses the infinitive: стоит сделать / стоит пойти.
Устроить is perfective because it suggests a single, completed action: arrange/set up (a break).
If you used устраивать (imperfective), it would sound more like in general / as a habit or focusing on process.

Перерывчик is a diminutive of перерыв (break). It adds a tone like:

• a little break
• a quick/short break
• often friendly, informal, “no big deal”

It’s stylistically casual. In formal contexts you’d typically say небольшой перерыв.

Yes, it’s somewhat “double-small,” but it’s common in casual speech for emphasis or tone:

• небольшой = objectively small
• -чик = emotionally “small/cute/quick”
  Together it can sound extra light and friendly: just a tiny little break.

Погулять is perfective and usually means to take a walk for a while (a bounded прогулка / some walking time).

• гулять (imperfective) = to be walking / to walk in general (process or habit)
  So немного погулять fits well: walk a bit (for a while).

The prefix по- often adds the idea “for a short time / a bit” with motion/activity verbs:

• поспать = sleep a bit
• поработать = work for a while
• погулять = walk for a while
  It naturally pairs with немного.

немного modifies the action: walk a little.
Both are possible, with slightly different emphasis:

• немного погулять = emphasis on a small amount of walking
• погулять немного = can sound a bit more conversational, emphasis later

Russian often omits repeated words. Here, стоит applies to both actions:

• Нам стоит [устроить…] и [погулять…].
  You can repeat it for clarity/emphasis, but it’s not necessary:
• Нам стоит устроить… и стоит немного погулять… (more deliberate/heavy)

в + location takes the prepositional case:

• парк → в парке
  This means in the park (location where you’ll walk).

Yes, and there’s a nuance:

• погулять в парке = walk in the park (general location)
• погулять по парку = walk around the park / through the park (movement across the area)

Both are natural; по парку can feel more like you’re wandering around inside it.

Common stresses here:

• нам стоИт
• устроИть
• небольшОй
• перерЫвчик
• погуля́ть
• в пАрке