Ben kitapçıya gidiyorum.

No, Ben is not necessary. The verb ending -yorum already marks the subject as I.

• Ben kitapçıya gidiyorum. = Kitapçıya gidiyorum. = I am going to the bookstore.

You include Ben:

• to emphasize the subject: I (as opposed to someone else) am going.
• in contrastive contexts: Ben kitapçıya gidiyorum, sen nereye gidiyorsun? – I’m going to the bookstore, where are you going?

In neutral, everyday speech, people very often drop Ben and just say Kitapçıya gidiyorum.

The -ya is the dative case ending, meaning to / toward.

• kitapçı = bookstore / bookseller
• kitapçı + (y)a → kitapçıya = to the bookstore

In general:

• dative suffix: -(y)a / -(y)e (to, toward)
• it attaches to nouns to show direction or goal:
  
  • okul (school) → okula (to school)
  • ev (house) → eve (to home)
  • arkadaş (friend) → arkadaşa (to the friend)

The y is a buffer consonant used when the noun ends in a vowel (like kitapçı).

This is vowel harmony.

The dative ending has two main forms: -a and -e (with a possible y in front after a vowel: -(y)a / -(y)e).

Rule (simplified):

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

In kitapçı:

• vowels are i – a – ı; the last vowel is ı (a back vowel)
• so we choose -a, not -e
• kitapçı + y + a → kitapçıya

These three are easy to mix up:

• kitap = book

  • kitaplar = books

• kitapçı = literally book-person → in practice:

  • bookseller (the person), or
  • bookstore / bookshop (the shop)

• kütüphane = library (a place where you borrow or read books, not buy them)

So:

• Ben kitapçıya gidiyorum. = I am going to the bookstore.
• Ben kütüphaneye gidiyorum. = I am going to the library.

The normal, neutral order in Turkish is Subject – (time) – place – object – verb:

• Ben kitapçıya gidiyorum.
  • Ben (subject)
  • kitapçıya (place, direction)
  • gidiyorum (verb)

However, Turkish word order is flexible for emphasis. You can say:

• Kitapçıya gidiyorum ben. → emphasizes ben (I)
• Ben gidiyorum kitapçıya. → sounds marked/emphatic; it suggests a contrast or some special focus (e.g. answering “Where exactly are you going?”)

For a simple, neutral statement, Ben kitapçıya gidiyorum (or just Kitapçıya gidiyorum) is the most natural.

The verb is gitmek = to go, but its stem behaves a bit irregularly in some forms.

1. Consonant change (t → d)
   The underlying stem is historically gid-. In some forms, the t appears, in others the d:

   • gitmek (infinitive)
   • gidiyorum (I am going)
   • gidiyor (he/she/it is going)
   • giderim (I go / I will go)

   So:

   • git- + -iyor + -um → gidiyorum (with t → d)

2. No extra personal ending
   The present continuous is formed as:

   • stem + -iyor + personal ending

   For I:

   • gidiyor + um → gidiyorum

   You do not add another “I” ending after that; -um already marks the subject:

   • gidiyorum = correct
   • × gidiyorumum = wrong

Full present continuous of gitmek:

• gidiyorum – I am going
• gidiyorsun – you are going
• gidiyor – he/she/it is going
• gidiyoruz – we are going
• gidiyorsunuz – you (pl./formal) are going
• gidiyorlar – they are going

Gidiyorum primarily corresponds to the English present continuous (I am going), but in Turkish it is also widely used for near-future plans, just like in English.

Examples:

• Şimdi kitapçıya gidiyorum.
  I am going to the bookstore now. (right now)

• Yarın kitapçıya gidiyorum.
  I am going to the bookstore tomorrow. (planned future action)

So Ben kitapçıya gidiyorum can mean:

• “I am (in the process of) going to the bookstore now.”
  or, with appropriate context/time word,
• “I’m going to the bookstore (later / tomorrow / this afternoon).”

Turkish does not have separate words for “a/an” and “the” like English does.

• kitapçıya gidiyorum can translate as:
  • I’m going to the bookstore
  • I’m going to a bookstore

Context usually tells you whether it’s specific or not.

If you want to make “a bookstore” explicit (indefinite), you can add bir:

• Bir kitapçıya gidiyorum.
  I’m going to a (some) bookstore.

If you want to stress that it’s a known/particular bookstore (like that bookstore), you can show it via context, or with a demonstrative:

• Şu kitapçıya gidiyorum. – I’m going to that bookstore.
• O kitapçıya gidiyorum. – I’m going to that/the bookstore (over there/known one).

Yes, Kitapçıya gidiyorum is a perfectly complete and very natural sentence.

• The personal ending -um in gidiyorum already encodes I.
• Dropping subject pronouns is normal and frequent in Turkish.

So:

• Ben kitapçıya gidiyorum. – more explicit, can be emphatic.
• Kitapçıya gidiyorum. – neutral, what you’d often say in everyday conversation.

Gitmek is a general verb meaning “to go”, not specifically “to walk”.

• Ben kitapçıya gidiyorum.
  I’m going to the bookstore. (by any means: walking, driving, taking the bus, etc.)

If you want to specify walking, you can add a manner expression:

• Kitapçıya yürüyerek gidiyorum.
  I am going to the bookstore on foot / by walking.

So gitmek focuses on the idea of going / moving from one place to another, not the mode of transport.