Learn Hardcore Russian: Сын же мечтает посмотреть, как обезьяна прыгает по веткам в своей клетке. - My son, however, dreams of watching how a monkey jumps on branches in its cage.

Сын мечтает посмотреть… – neutral: The son dreams of watching…
Сын же мечтает посмотреть… – The son, however, dreams of watching… / The son, for his part, dreams of watching…

It often implies contrast with something mentioned earlier, e.g.:

Дочка боится обезьян, сын же мечтает посмотреть…
The daughter is afraid of monkeys, whereas the son dreams of watching…

You can drop же grammatically; you’ll just lose that contrastive/emphatic flavor.

Why is it мечтает посмотреть and not мечтает смотреть?

Both are possible, but they feel different:

мечтать посмотреть (perfective infinitive) – to dream of (once) watching it at some point in the future, a specific eventual act of watching.
мечтать смотреть (imperfective infinitive) – to dream of engaging in watching as an activity (e.g. having the opportunity to observe monkeys in general). This usage is less common here and sounds a bit off in this specific sentence.

In this context, the son dreams of actually seeing this happen at least once, so Russian prefers мечтает посмотреть with the perfective.

Why is there a comma before как in мечтает посмотреть, как обезьяна прыгает…?

Here как introduces a subordinate clause that depends on посмотреть:

Main part: Сын же мечтает посмотреть – The son dreams of watching.
Subordinate clause: как обезьяна прыгает по веткам… – how the monkey jumps from branch to branch…

In Russian, when как introduces a full clause (with its own subject and verb) that explains what or how exactly you will see, you usually separate it with a comma:

Он любит смотреть, как солнце садится.
Я помню, как мы гуляли по парку.

So the comma here is mandatory.

The son will watch this in the future, so why is it как обезьяна прыгает, not как обезьяна будет прыгать?

Russian uses present tense in the subordinate clause to describe an action that is simultaneous with a future (or infinitive) action in the main part:

мечтает посмотреть, как обезьяна прыгает…

Literally: dreams to watch how the monkey jumps…
But functionally: dreams of watching the monkey jump… (when he gets the chance)

Будет прыгать would stress the future-ness of the monkey’s jumping itself and sound more like a prediction:

Он думает, как обезьяна будет прыгать, когда её выпустят.
He wonders how the monkey will jump when they let it out.

In your sentence, we just need the normal, ongoing action that will be observed, so the simple present прыгает is natural.

Why is it прыгает (imperfective) and not прыгнет or попрыгает?

Aspect here shows the type of action being watched:

прыгает (imperfective, present) – ongoing or repeated action: is jumping / jumps around.
прыгнет (perfective, future) – a single jump in the future: will jump once.
попрыгает (perfective with по-) – will jump for a while.

He wants to watch the general process: the monkey jumping around on the branches, not just one jump or a short episode. That’s why Russian uses imperfective прыгает.

What case is по веткам, and why is по used here?

По веткам = по + dative plural of ветка (ветка → веткам).

With movement verbs, по + dative often means “over / along / around multiple objects or surfaces”:

идти по улице – to walk along the street
бегать по полю – to run around the field
прыгать по веткам – to jump around on / from branch to branch

So прыгает по веткам suggests the monkey has many branches and is moving among them, not just on one single branch.

Could we say прыгает на ветках instead of по веткам? What’s the difference?

You could say прыгает на ветках, but the nuance changes:

прыгает по веткам – moving from branch to branch, around the branches in general. Focus on movement through a set of branches.
прыгает на ветках – literally jumps on the branches; more static-sounding, focusing on being located on branches while jumping, less on moving from one to another.

In natural Russian, прыгать по веткам is the more idiomatic way to describe a monkey moving actively from branch to branch.

In в своей клетке, what does своей refer to – the son or the monkey?

Своей refers to the subject of its own clause:

Clause: как обезьяна прыгает по веткам в своей клетке
Subject of this clause: обезьяна

So в своей клетке means “in its own cage”, i.e. the monkey’s cage, not the son’s.

Rule of thumb: свой / своя / своё / свои normally refers back to the subject of the clause it’s in, not to the subject of the whole sentence.

Why use своей, not его or её in в своей клетке?

Свой is a reflexive possessive pronoun: it means “one’s own” and avoids ambiguity.

обезьяна прыгает по веткам в своей клетке
→ clearly: in its own cage.
обезьяна прыгает по веткам в её клетке
→ could mean: in *her cage* (some other female’s cage, not necessarily the monkey’s).

Russian prefers свой whenever the possessor is the subject of that clause, especially to avoid confusion about whose cage it is.

What form is своей here, and how does it agree with клетке?

Своей is the feminine, singular, prepositional form of свой.

Agreement:

клетка – feminine, singular noun.
After в (with “in”), location is expressed by the prepositional case: в клетке.
So свой must also be feminine singular prepositional → в своей клетке.

Pattern:

мой / твой / свой / наш / ваш / их all decline and agree in gender, number, and case with the noun they modify.

Could we just say Сын мечтает посмотреть… without же? Does that change the meaning much?

Yes, you can say:

Сын мечтает посмотреть, как обезьяна прыгает по веткам в своей клетке.

This is perfectly correct and means the same in basic content.

Adding же:

Adds contrast or “separate topic” feeling: The son, however, dreams of watching…
Often implies comparison to someone else (e.g. daughter, parents) who have a different attitude.

So же doesn’t change the literal event; it changes the discourse nuance (contrast/emphasis).

Why is it мечтает посмотреть, not мечтает о том, чтобы посмотреть?

Both exist, but they differ in style and feel:

мечтать + infinitive:
Сын мечтает посмотреть… – simple, natural, colloquial/neutral: The son dreams of watching…
мечтать о том, чтобы + infinitive:
Сын мечтает о том, чтобы посмотреть… – more formal, heavy, or emotional; used when you want to stress the dream as a wish or goal.

In everyday speech, especially with a short, concrete action like посмотреть, Russian prefers the compact infinitive construction.

What exactly does как mean here in посмотреть, как обезьяна прыгает…? Is it literally “how”?

Literally, как = how, but in this pattern it often just introduces the content of what you see, and in English we might translate more naturally as a participial phrase:

мечтает посмотреть, как обезьяна прыгает по веткам…
→ dreams of watching *the monkey jumping from branch to branch in its cage.*

So:

Russian: посмотреть, как [subject + verb]
English: to watch [subject + -ing form]

It’s still “how” in a grammatical sense, but in English we don’t always preserve the word how in translation.