Learn Hardcore Russian: После работы я хочу сделать паузу и отдохнуть. - After work I want to take a break and rest.

Я хочу сделать паузу. – I want to (take) a break (once, now).
Я люблю делать паузу каждый час. – I like taking a break every hour (habitually, repeatedly).

Why is it отдохнуть and not отдыхать?

Again, this is aspect:

отдохнуть – perfective, “to get (some) rest, to have rested” (completed result)
отдыхать – imperfective, “to rest / to be resting” (process)

With хочу, both are possible, but they mean slightly different things:

Я хочу отдохнуть. – I want to rest (and finish resting, feel rested).
Я хочу отдыхать. – I want to be in a state of resting / to spend time resting (e.g., on vacation, in general).

In your sentence, сделать паузу и отдохнуть fits well because both verbs point to completed actions during that break.

Why can Russian say я хочу сделать паузу и отдохнуть with infinitives after хочу?

The verb хотеть is typically followed by an infinitive:

я хочу сделать – I want to do
я хочу отдохнуть – I want to rest

Pattern:
[subject] + хотеть + infinitive

So:

Я хочу есть. – I want to eat.
Я хочу спать. – I want to sleep.
Я хочу поехать. – I want to go (by transport).

In your sentence, there are two infinitives linked by и:

сделать (паузу) and отдохнуть
both depend on хочу (I want to take a break and to rest).

What case is паузу and why does it end with -у?

Паузу is accusative singular of the feminine noun пауза.

For many feminine nouns in -а:

Nominative: пауза
Accusative singular (direct object): паузу

You use the accusative case for the direct object of the verb:

сделать что? – паузу
читать книгу
купить машину

So сделать паузу = “to make (do) a pause / break” where паузу is the thing being “made” (direct object).

Is the word order fixed, or can I say this sentence in another way?

Russian word order is relatively flexible. These variants are all possible and natural:

После работы я хочу сделать паузу и отдохнуть. (your version – neutral)
Я хочу после работы сделать паузу и отдохнуть.
Я хочу сделать паузу и отдохнуть после работы.

The meaning is basically the same. Minor differences:

Putting после работы at the beginning sounds like you’re setting the time frame first (After work, I want…).
Putting после работы at the end can slightly emphasize when you want to rest.

Can I omit я and just say После работы хочу сделать паузу и отдохнуть?

Yes. In Russian, subject pronouns are often omitted when the verb ending makes the subject clear.

(Я) хочу сделать паузу.
(Я) устал.

So:

После работы хочу сделать паузу и отдохнуть. – completely natural in speech and writing.

Including я is also fine; it may sound a bit more explicit or slightly more emphatic on I.

Why is there an и between сделать паузу and отдохнуть instead of a comma or something else?

Here и is just the normal coordinating conjunction and linking two infinitives that share the same subject and verb хочу:

я хочу [сделать паузу] и [отдохнуть]

It works exactly like English “and” in:

I want to take a break and rest.

Using a comma here would be incorrect; Russian uses a conjunction (like English) to join parallel infinitives in such a structure.

What is the difference between пауза and перерыв? Could I say сделать перерыв?

Yes, сделать перерыв is also possible, but there is a nuance:

пауза – a pause, often shorter, can be in speech, in music, or just a small break in activity.
перерыв – a break, often regular/scheduled or more “official”: lunch break, lesson break, etc.

Examples:

Сделать паузу и помолчать. – To pause and be silent.
Сделать перерыв в работе. – To take a break from work (often longer, more formal).

In your sentence, both сделать паузу and сделать перерыв work; пауза can sound a bit more casual or “small rest,” but context decides.

How do I pronounce these words, and where is the stress?

Stresses (the stressed vowel is in capitals in transliteration):

после – по́сле – PO-sle
работы – рабо́ты – ra-BO-ty
я – я – ya
хочу – хочу́ – ha-CHU
сделать – сде́лать – SDYE-latʹ
паузу – па́узу – PA-u-zu
и – и – ee
отдохнуть – отдохну́ть – at-dakh-NUTʹ

Correct stress is important because it often changes the vowel quality in unstressed positions.

Could I say Когда я закончу работу, я хочу сделать паузу и отдохнуть instead of После работы…?

Yes, and it is perfectly natural.

После работы я хочу… – After work I want…
Когда я закончу работу, я хочу… – When I finish work, I want…

Both express the time relationship.
После работы is shorter and more typical; когда я закончу работу makes the idea of finishing more explicit but doesn’t change the basic meaning in this context.