Kad imam mučninu, pijem samo vodu.

Yes. Kad and kada both mean when.

• kad is shorter and very common in everyday speech
• kada is a bit fuller and can sound slightly more formal or careful

So Kad imam mučninu, pijem samo vodu. and Kada imam mučninu, pijem samo vodu. both work.

Croatian often expresses physical states with imati + a noun.

So:

• imam mučninu = literally I have nausea
• natural English meaning = I feel nauseous / I have nausea

This is a normal Croatian pattern. English often uses an adjective where Croatian uses a noun phrase.

Mučninu is in the accusative singular.

That is because it is the direct object of imam (I have).

The base form is:

• mučnina = nausea

Accusative singular:

• mučninu

This is a very common feminine noun pattern:

• nominative: -a
• accusative singular: -u

For the same reason: vodu is the direct object of pijem (I drink).

Base form:

• voda = water

Accusative singular:

• vodu

So in the sentence:

• imam mučninu = I have nausea
• pijem vodu = I drink water

Both nouns are objects, so both are in the accusative.

Pijem is the imperfective verb, and that fits well here because the sentence describes a repeated or usual action:

• Kad imam mučninu, pijem samo vodu.
• When I feel nauseous, I only drink water.

This sounds habitual: whenever that situation happens, this is what I do.

Popijem is perfective and usually points to a completed action, more like I drink up / I have a drink / I end up drinking in a single instance. That would change the feel of the sentence.

Not only the present moment. In this sentence, the present tense expresses a general habit or repeated situation.

So:

• imam = when I have / when I get
• pijem = I drink

Together they mean something like:

• Whenever I feel nauseous, I only drink water

This is very common in Croatian, just as in English.

Because Kad imam mučninu is a subordinate clause placed before the main clause.

Structure:

• Kad imam mučninu = subordinate clause
• pijem samo vodu = main clause

Croatian normally uses a comma here, just like English often does with When I feel nauseous, I only drink water.

Because Croatian usually does not need subject pronouns when the verb ending already shows who the subject is.

Here:

• imam = I have
• pijem = I drink

So ja is unnecessary unless you want emphasis or contrast.

For example:

• Ja pijem samo vodu, a on čaj.
• I only drink water, and he drinks tea.

Samo means only / just.

In this sentence, it modifies vodu in meaning:

• pijem samo vodu = I drink only water

Its position before the noun is very natural in Croatian.

You may also hear:

• samo pijem vodu

That can also work, but it may put slightly more focus on the action or on the restriction. In this sentence, pijem samo vodu is the most straightforward choice.

It is understandable and correct, but many speakers would very often say:

• Kad mi je muka, pijem samo vodu.

This is extremely common for when I feel sick / nauseous.

A few possibilities are:

• imam mučninu = I have nausea
• mučno mi je = I feel nauseous
• muka mi je = I feel sick / nauseous

So your sentence is fine, but a learner may also want to recognize these more idiomatic alternatives.

Yes. In a sentence about repeated behavior, kad often has the sense of whenever.

So this sentence can be understood as:

• When I feel nauseous, I only drink water
• Whenever I feel nauseous, I only drink water

Both are good English translations depending on context.