Ablam ve ağabeyim gelince, ikisine de çay vereceğim.

Ablam means my older sister, and ağabeyim means my older brother.

The endings -m / -im are 1st person singular possessive endings, meaning my.

• abla = older sister

• ablam = my older sister

• ağabey = older brother
• ağabeyim = my older brother

Turkish often uses possessive endings instead of a separate word like my.

No. These words specifically mean older siblings:

• abla = older sister
• ağabey / abi = older brother

If you just want to say sister or brother in a more general sense, Turkish also has:

• kız kardeş = sister
• erkek kardeş = brother

So ablam ve ağabeyim is specifically my older sister and my older brother.

Gelince comes from gelmek (to come) plus the suffix -ince.

Here it means something like:

• when ... comes
• when ... come
• once ... come

So:

• Ablam ve ağabeyim gelince = When my older sister and older brother come / Once they come

This -ince form is often used for time clauses.

Examples:

• Eve gelince beni ara. = Call me when you get home.
• Onu görünce sevindim. = I was happy when I saw him/her.

Because gelince is not a fully conjugated tense verb like an English finite verb. It is a converb / adverbial verb form.

That means it does not change for person or number in the way a normal main verb does.

So even with a plural subject, Turkish still says:

• Ablam ve ağabeyim gelince...

not something like a separate plural form of gelince.

The subject itself already tells you that more than one person is involved.

İkisine means to the two of them.

It is built from:

• iki = two
• ikisi = the two of them / the two ones
• ikisine = to the two of them

The ending -e / -a is the dative case, often meaning to.

So:

• ikisine = to both of them / to the two of them

This is used because vermek (to give) normally takes something given and the person it is given to.

Here, de adds the sense of both or each one too.

So ikisine de means:

• to both of them
• to each of the two

It is very common in Turkish to use de like this after words such as:

• ikisine de = to both of them
• üçüne de = to all three
• hepsine de = to all of them

This de is not exactly the same as English too in translation, but it has a similar additive feeling.

Because çay here is an indefinite direct object.

In Turkish, a direct object usually takes the accusative ending only if it is definite / specific.

So:

• çay vereceğim = I will give tea / some tea
• çayı vereceğim = I will give the tea (a specific tea)

In this sentence, the speaker is just saying they will serve tea, not a particular already-identified tea.

Vereceğim comes from vermek (to give).

It breaks down like this:

• ver- = give
• future marker: -(y)ecek / -(y)acak
• -im / -ım / -um / -üm = I

So:

• verecek = will give
• vereceğim = I will give

The extra -y- appears because of how the verb stem and suffix connect.

Because the verb agrees with the speaker, not with the people receiving the tea.

The subject of vereceğim is hidden but understood:

• (Ben) vereceğim = (I) will give

The two siblings are not the subject of this verb; they are the indirect object:

• ikisine de = to both of them

So the sentence means: When my older sister and older brother come, I will give tea to both of them.

The comma separates the time clause from the main clause:

• Ablam ve ağabeyim gelince, = When my older sister and older brother come,
• ikisine de çay vereceğim. = I will give tea to both of them.

In Turkish, punctuation here works much like in English. The comma helps show that the first part sets the time/context for the main action.

Yes. Turkish word order is flexible, although some versions sound more natural in certain contexts.

The original sentence is very natural:

• Ablam ve ağabeyim gelince, ikisine de çay vereceğim.

You could also say:

• Ablam ve ağabeyim gelince çay vereceğim ikisine de.

But this sounds more marked or conversational.

A more standard pattern in Turkish is to place the verb at the end, which the original sentence does:

• time/context
• objects/complements
• verb

So the original sentence is a very good neutral model.

Usually no. In this sentence, gelince means when or once, not if.

• gelince = when/once (they) come
• gelirlerse = if they come

So there is a clear difference:

• Ablam ve ağabeyim gelince... = When my older sister and older brother come...
• Ablam ve ağabeyim gelirlerse... = If my older sister and older brother come...

The first one assumes their arrival as the time reference. The second one makes it conditional.

In careful or standard Turkish, ağabeyim is perfectly correct.

In everyday speech, many people say:

• abi = older brother
• abim = my older brother

So in casual speech, you may hear:

• Ablam ve abim gelince...

That is very common and natural in conversation.
But ağabeyim is still correct and useful to know.

Yes, you could say:

• Ablam ve ağabeyim gelince, onlara çay vereceğim.

That means: When my older sister and older brother come, I will give them tea.

The difference is:

• onlara = to them
• ikisine de = to both of them

So ikisine de is a little more explicit and emphasizes that the tea is for each of the two.