Kiam ajn mi estas laca, mi trinkas varman teon.

Kiam ajn means whenever or any time that.

It is made of:

• kiam = when
• ajn = a particle that adds the sense of ever / any ... at all

So kiam ajn mi estas laca literally means something like when-ever I am tired, or more naturally, whenever I am tired.

It is written as two separate words because ajn is its own particle in Esperanto and can combine with several question/correlative words:

• kiu ajn = whoever / any one who
• kie ajn = wherever
• kiel ajn = however
• kiam ajn = whenever

Yes, you could, but the meaning changes a little.

• Kiam mi estas laca, mi trinkas varman teon. = When I am tired, I drink hot tea.
• Kiam ajn mi estas laca, mi trinkas varman teon. = Whenever I am tired, I drink hot tea.

With ajn, the sentence sounds more general and habitual: every time this happens.

Without ajn, it can still be understood generally, but it may sound a bit less emphatic.

Because laca is a predicate adjective, not a direct object.

After esti (to be), adjectives describe the subject and do not take -n.

So:

• mi estas laca = I am tired

Compare that with a direct object:

• mi trinkas teon = I drink tea

Here teon gets -n because it is the thing being drunk.

A useful rule:

• after esti: no accusative on the adjective
• direct object: accusative -n

Because teon is the direct object, and varman is an adjective describing that noun.

In Esperanto, adjectives agree with the nouns they describe in both:

• number: singular/plural
• case: especially the accusative -n

So:

• teo = tea
• teon = tea as a direct object
• varma teo = hot tea
• varman teon = hot tea as a direct object

The adjective must match the noun:

• varma teo
• varmaj teoj
• varman teon
• varmajn teojn

Because it is the direct object of trinkas.

Ask: What do I drink? Answer: varman teon

In Esperanto, the direct object normally takes -n:

• Mi vidas la hundon. = I see the dog.
• Mi manĝas pomon. = I eat an apple.
• Mi trinkas teon. = I drink tea.

So in your sentence:

• mi trinkas varman teon = I drink hot tea

Because Esperanto has no indefinite article.

English distinguishes:

• a tea
• the tea

Esperanto only has a definite article:

• la = the

So:

• teo can mean tea or a tea, depending on context
• la teo = the tea

That means:

• mi trinkas varman teon = I drink hot tea or I drink a hot tea, depending on context

In this sentence, English naturally uses hot tea without an article.

Because in Esperanto, adjectives that describe the subject after esti usually come after the verb, just like in English:

• mi estas laca = I am tired
• la vetero estas bela = the weather is beautiful

You normally would not say mi laca estas in ordinary neutral Esperanto. Word order can sometimes be changed for style or emphasis, but mi estas laca is the normal form.

Yes, you can move them around.

These are all possible:

• Kiam ajn mi estas laca, mi trinkas varman teon.
• Mi trinkas varman teon, kiam ajn mi estas laca.

Both mean essentially the same thing. The first version puts the time condition first, which is very natural here.

Inside the second clause, word order is also somewhat flexible because Esperanto marks the direct object with -n:

• Mi trinkas varman teon.
• Varman teon mi trinkas.

But the first one is the most neutral and common.

Usually varma means warm or hot, depending on context.

So varman teon can often be translated as:

• warm tea
• hot tea

If you want to be especially clear that it is very hot, context usually does the job. In many everyday situations, varma teo is a perfectly normal way to say hot tea.

Because tea here is being treated as an uncountable substance, just as in English.

So:

• teo = tea
• teoj = teas, kinds of tea, or separate servings in some contexts

In this sentence, the natural idea is simply I drink hot tea, so singular teon is correct.

If you said teojn, it would sound like teas in English, which is a different idea.

It normally expresses a general habit.

Because of:

• kiam ajn = whenever
• the present tense estas / trinkas

the sentence means something like:

• Whenever I am tired, I drink hot tea
• Any time I’m tired, I drink hot tea

So it describes what the speaker generally does, not just what is happening right now.

Ajn is pronounced as one syllable.

A rough English approximation is something like eye-n or aye-n, but very short and smooth.

More exactly:

• a like the a in father
• j like English y
• n as usual

So ajn sounds roughly like ahyn in one syllable.

And kiam ajn is roughly:

• KEE-am ayn

Not perfect English-based spelling, but close enough to get started.