После кардио мне хочется пить воду.

Yes, после normally requires the genitive case.

So the pattern is:

• после тренировки = after the workout
• после урока = after the lesson

In your sentence, кардио does not change because it is a very common indeclinable loanword. That means its form stays the same in all cases.

So:

• nominative: кардио
• genitive after после: still кардио

That is why После кардио is correct.

Мне is the dative case of я.

Russian often uses the dative with impersonal expressions that describe a person’s feeling, state, or experience. In this construction, the person is not treated as a normal grammatical subject the way English does.

So:

• я хочу = I want
• мне хочется = I feel like / I want

A very literal way to think of мне хочется is something like:

• to me, it is wanted
• or more naturally, I feel like it

So мне is correct because the sentence uses an impersonal pattern.

Хочется comes from хотеться, which means to feel like, to want, or to have a desire to.

It is different from хотеть in tone:

• я хочу = I want
• мне хочется = I feel like / I have a desire to / I’m craving

So хочется often sounds a bit softer, less direct, and more like a natural feeling rather than a firm decision.

In this sentence:

• мне хочется пить воду = I feel like drinking water

Both can be translated as I want to drink water, but the nuance is different.

• я хочу пить воду = a more direct, straightforward statement of want
• мне хочется пить воду = more like I feel like drinking water, I’m craving water, or I’m in the mood for water

After exercise, мне хочется is especially natural because it can describe a physical feeling or urge.

So after cardio:

• я хочу пить воду = I want to drink water
• мне хочется пить воду = I feel like drinking water / I’m really in the mood for water

Because хочется is commonly followed by an infinitive that names the action someone feels like doing.

This is a very common Russian pattern:

• мне хочется спать = I feel like sleeping / I’m sleepy
• мне хочется есть = I feel like eating / I’m hungry
• мне хочется гулять = I feel like going for a walk
• мне хочется пить воду = I feel like drinking water

So пить is the action being desired.

Because воду is the accusative case, and it is the direct object of пить.

You are drinking what?
→ воду

Compare:

• вода = water (subject form, nominative)
• воду = water (object form, accusative)

So:

• Вода холодная. = The water is cold.
• Я пью воду. = I am drinking water.

In your sentence, воду is correct because it is the thing being drunk.

Yes, but the nuance changes.

• пить воду = drink water
• пить воды = drink some water

The form воды here is genitive and often has a partitive meaning: not water in general as an object, but some amount of water.

So these feel slightly different:

• мне хочется пить воду = I feel like drinking water
• мне хочется попить воды = I feel like having some water

In everyday speech, воды is often very natural when someone means some water.

Very often, yes.

Russian commonly uses хочется пить to express thirst:

• Мне хочется пить. = I’m thirsty.

So your sentence can feel close to:

• После кардио мне хочется пить. = After cardio, I’m thirsty.

When you add воду, you make it more specific:

• После кардио мне хочется пить воду. = After cardio, I feel like drinking water.

So it expresses thirst, but with the extra detail that water is what you want.

Your sentence is understandable and natural enough, especially if you want to emphasize water specifically.

But native speakers might also say:

• После кардио мне хочется пить. = After cardio, I’m thirsty.
• После кардио мне хочется воды. = After cardio, I want some water.
• После кардио мне хочется попить воды. = After cardio, I feel like drinking some water.

These alternatives are very common.

Your original sentence is fine, but it is a bit more explicit than Russian often needs to be.

Yes. Russian word order is flexible, and changing it usually changes emphasis, not the core meaning.

Your version:

• После кардио мне хочется пить воду.

This puts После кардио first, which sets the context right away: after cardio.

Other possible orders:

• Мне после кардио хочется пить воду.
• После кардио хочется пить воду.
• Пить воду после кардио мне хочется. — more emphatic or marked

The first version is very natural because it starts with the situation, then gives the feeling.

Because Russian has no articles like the or a/an.

Russian usually expresses those ideas through:

• context
• word order
• case choice
• sometimes vocabulary

So:

• воду can mean water, the water, or just water in general, depending on context
• воды can sometimes suggest some water

English needs articles, but Russian does not.

That is why пить воду is completely normal without any extra word before воду.