Bu akşam iki aktarma yapacağım; biri metrobüsten metroya, diğeri metrodan otobüse.

Yes. Literally, aktarma yapmak is to make/do a transfer, but in natural English we usually say to transfer or to make a connection.

In Turkish, many everyday actions are expressed with a noun + yapmak. So:

• aktarma yapmak = to make a transfer
• alışveriş yapmak = to do shopping
• spor yapmak = to do sports/exercise

So iki aktarma yapacağım means I will make two transfers.

Yapacağım comes from yapmak and means I will do / I am going to do.

It can be broken down like this:

• yap- = do, make
• -acak / -ecek = future tense
• -ım / -im / -um / -üm = I

So:

• yapacağım = I will do

Because of sound changes, it is not simply yapacakım. Turkish regularly changes the form when suffixes are added, so yapacak + ım becomes yapacağım.

After numbers, Turkish nouns normally stay singular.

So:

• iki aktarma = two transfers
• üç kitap = three books
• beş öğrenci = five students

Using a plural ending after a number is usually incorrect in standard Turkish. This is very different from English, where you must say two transfers, three books, and so on.

Bu akşam means this evening / tonight.

• bu = this
• akşam = evening

Time expressions in Turkish often appear without any case ending when they simply tell you when something happens:

• Bugün geliyorum. = I’m coming today.
• Yarın çalışacağım. = I’ll work tomorrow.
• Bu akşam iki aktarma yapacağım. = Tonight I’ll make two transfers.

So bu akşam is just a time expression in its basic form.

They mean one (of them) and the other.

In this sentence:

• biri metrobüsten metroya = one is from the metrobüs to the metro
• diğeri metrodan otobüse = the other is from the metro to the bus

So the speaker is listing the two transfers one by one.

A useful way to understand them:

• biri = one of them
• diğeri = the other one

You may also hear birisi in Turkish, but biri is very common and natural.

These endings show from and to.

From: ablative case

• -den / -dan / -ten / -tan = from

So:

• metrobüsten = from the metrobüs
• metrodan = from the metro

To: dative case

• -e / -a = to, toward

So:

• metroya = to the metro
• otobüse = to the bus

This is a very common transport pattern in Turkish:

• otobüsten metroya = from the bus to the metro
• evden işe = from home to work
• okuldan eve = from school to home

Because Turkish often inserts a buffer consonant when a suffix beginning with a vowel is added to a word that already ends in a vowel.

Metro ends in -o, and the dative ending here is -a / -e. Turkish does not like metroa, so it adds y:

• metro + a → metroya

This y is very common:

• araba + a → arabaya
• masa + ı → masayı
• bile + e → bileye would not be typical as a lexical item, but the same linking principle applies

So metroya simply means to the metro.

This is because of vowel harmony.

The dative ending has two main forms:

• -a
• -e

Which one you use depends on the vowels in the word. Since otobüs has front vowels like ü, it takes -e:

• otobüs → otobüse

Similarly:

• ev → eve
• okul → okula
• şehir → şehre

So otobüse is the correct vowel-harmony form of to the bus.

Turkish often leaves out words that are easy to understand from context.

The full idea is something like:

• Biri metrobüsten metroya aktarma, diğeri metrodan otobüse aktarma.
• or more naturally, Birini metrobüsten metroya, diğerini metrodan otobüse yapacağım.

But Turkish often omits repeated material when it is obvious. In your sentence, after iki aktarma yapacağım, the listener already knows we are talking about the two transfers. So the shorter version sounds natural.

This kind of omission is very common in Turkish.

The semicolon separates the main statement from the explanation/list that follows.

• Bu akşam iki aktarma yapacağım = main statement
• biri metrobüsten metroya, diğeri metrodan otobüse = explanation of what those two transfers are

In English, you might also use:

• a colon
• a dash
• or even a full stop

In Turkish writing, a semicolon works well here because the second part is closely connected to the first.

The given sentence is natural, but Turkish word order is fairly flexible.

The basic sentence:

• Bu akşam iki aktarma yapacağım.

could also become:

• İki aktarma yapacağım bu akşam.
• Bu akşam yapacağım iki aktarma...
  though this starts to sound more marked or literary depending on context

The original order is neutral and clear:

• time first: Bu akşam
• quantity/object: iki aktarma
• verb: yapacağım

That is a very common Turkish pattern.

Yes, you often can.

• biri = one of them
• birisi = one of them / someone / one

In many contexts, both are possible. Here, biri sounds very natural and compact. Turkish often prefers the shorter form in everyday speech.

So these are both understandable:

• biri metrobüsten metroya
• birisi metrobüsten metroya

But biri is probably the more natural choice in this sentence.

Yes. Metrobüs is just the name of a transport system, and grammatically it behaves like a regular noun.

So it can take case endings normally:

• metrobüs = the metrobüs
• metrobüse = to the metrobüs
• metrobüsten = from the metrobüs

For a learner, the important point is that even transport names like metro, otobüs, and metrobüs take regular Turkish case endings when you want to say to, from, and so on.