Ben çayı limonla içiyorum.

Yes. Ben means I, but Turkish often drops subject pronouns because the verb ending already shows the person.

• içiyorum = I am drinking / I drink
• So Çayı limonla içiyorum is also a complete sentence.

Including ben can add emphasis, such as:

• Ben çayı limonla içiyorum. = I drink tea with lemon.
  (maybe contrasting with someone else)

Because it is the direct object of the verb, and in Turkish a specific/definite direct object usually takes the accusative ending.

• çay = tea
• çayı = the tea / tea (as a specific object)

So:

• Çay içiyorum = I drink tea / I’m drinking tea.
  (more general, non-specific)
• Çayı içiyorum = I’m drinking the tea / I’m drinking that tea.
  (specific)

Also, the extra y is a buffer consonant added between two vowels:

• çay + ı → çayı

This is a very common question for English speakers, because English does not mark this in the same way.

• çay içiyorum = I drink tea / I’m drinking tea
  This is more general or indefinite.
• çayı içiyorum = I’m drinking the tea / that tea
  This points to a specific tea.

In Turkish, the accusative often signals that the object is definite or specific.

Limonla means with lemon.

It is formed from:

• limon = lemon
• -la / -le = with

So:

• limon + la = limonla = with lemon

This ending comes from ile, which also means with. So you may also see:

• limon ile

But limonla is the more natural, compact form in everyday Turkish.

Because of vowel harmony.

The suffix -la / -le changes depending on the last vowel of the word.

• If the last vowel is a back vowel (a, ı, o, u), use -la
• If the last vowel is a front vowel (e, i, ö, ü), use -le

The last vowel in limon is o, which is a back vowel, so:

• limonla is correct

Compare:

• şekerle = with sugar
  (last vowel e → -le)

Usually it means with lemon as something accompanying the tea.

In context, Ben çayı limonla içiyorum is naturally understood as:

• I drink tea with lemon.
• I have lemon in my tea.

The suffix -la/-le can mean with, and context tells you whether it means:

• accompaniment: limonla = with lemon
• instrument/means: like elle = with the hand
• together with someone/something

Here, the accompaniment meaning is the natural one.

İçiyorum breaks down like this:

• iç- = drink
• -iyor- = present continuous marker
• -um = I

So:

• içiyorum = I am drinking / I drink

This is a very useful pattern:

• geliyorum = I am coming
• yiyorum = I am eating
• okuyorum = I am reading

It can mean either, depending on context.

The Turkish -iyor form is often called the present continuous, but in real usage it can cover both:

• I am drinking
• I drink

So Ben çayı limonla içiyorum could mean:

• I am drinking tea with lemon.
  or
• I drink tea with lemon.

Context usually makes the intended meaning clear.

Because Turkish normally uses Subject–Object–Verb order.

This sentence is:

• Ben = subject
• çayı = object
• limonla = adverbial/complement
• içiyorum = verb

So the verb typically comes last.

That said, Turkish word order is flexible, and changing it can shift emphasis. For example:

• Ben çayı limonla içiyorum. = neutral
• Çayı ben limonla içiyorum. = I’m the one who drinks the tea with lemon.
• Limonla çayı içiyorum. = emphasis on with lemon

But the default pattern is to place the verb at the end.

No, Turkish does not have direct equivalents of English a/an and the as separate articles.

Instead, Turkish often shows these ideas through:

• context
• word order
• endings like the accusative
• words like bir when needed

In this sentence, çayı feels more like the tea / the specific tea, because of the accusative ending.

Compare:

• çay = tea / a tea / tea in general
• çayı = the tea / specific tea

That y is a buffer consonant.

When a Turkish word ending in a vowel is followed by a suffix beginning with a vowel, Turkish often inserts y to make pronunciation easier.

Here:

• çay ends in the vowel sound a
• the accusative suffix is -ı
• so Turkish inserts y

Result:

• çay + ı → çayı

You will see this in many other words too.

Yes, but it means something slightly different in structure.

• Ben çayı limonla içiyorum = I drink the tea with lemon.
• Ben limonlu çay içiyorum = I drink lemon tea / tea with lemon in it.

Here:

• limonla = with lemon
• limonlu = lemon-flavored / containing lemon

In many situations, both could describe a similar real-life idea, but grammatically they are built differently.