Ben başkasının kalemini kullanmıyorum.

Yes. Turkish verbs already show the subject, so ben is often optional.

• Kullanmıyorum already means I am not using / I don’t use.
• So Başkasının kalemini kullanmıyorum is a perfectly normal sentence.

Adding ben usually gives a little extra emphasis or contrast, like I’m not the one using someone else’s pen.

Başkasının means someone else’s or literally of someone else.

It comes from:

• başka = other / another
• başkası = someone else / another one
• başkasının = of someone else / someone else’s

So here, başkasının is the possessor: the pen belongs to someone else.

This is a very common Turkish pattern called the genitive-possessive construction.

In Turkish, possession is often shown in two places:

• the possessor gets the genitive ending
• the thing possessed gets a possessive ending

So:

• başkasının kalemi = someone else’s pen

Breakdown:

• başkasının = of someone else
• kalemi = his/her/its pen

This double marking is normal Turkish grammar.

Because the noun is the direct object of the verb, and it is specific/definite.

• kalemi = his/her pen
• kalemini = his/her pen as the direct object

The extra -ni here is the accusative form used after a 3rd-person possessed noun.

So:

• başkasının kalemi = someone else’s pen
• başkasının kalemini = someone else’s pen (as the thing being used)

Here is the structure:

• kalem = pen
• kalem-i = his/her/its pen
• kalem-i-ni = his/her/its pen + accusative

That middle -i is the 3rd person possessive ending.

The final -ni shows that the noun is the direct object of the verb. The n is a buffer consonant that appears in this kind of form.

It breaks down like this:

• kullan- = use
• -m- / -ma- = negation
• -iyor / -ıyor = present continuous
• -um = I

So kullanmıyorum means literally something like:

use + not + ongoing/present + I

In natural English, that becomes I am not using or I don’t use, depending on context.

It can mean either one, depending on context.

In Turkish, the present continuous form is often used more broadly than in English. So kullanmıyorum can mean:

• I’m not using it right now
• I don’t use it in general

If you wanted a more general, habitual sense, Turkish can also use the aorist, for example kullanmam. But in everyday speech, kullanmıyorum is very common and natural.

Because Turkish normally uses Subject–Object–Verb word order.

So this sentence follows the usual pattern:

• Ben = subject
• başkasının kalemini = object
• kullanmıyorum = verb

That is why the verb comes at the end.

Turkish word order is also flexible, though. You can move parts around for emphasis, but the basic neutral order is the one in this sentence.

Yes. Başka birinin kalemini kullanmıyorum is also correct.

The two are very close in meaning:

• başkasının = someone else’s
• başka birinin = another person’s / someone else’s

Başkasının is shorter and very common.
Başka birinin can sound a little more explicit because it clearly contains birinin = of someone / of one person.

Because başka by itself means other / another, but it does not automatically mean someone else’s.

Compare:

• başka kalem = another pen / a different pen
• başkasının kalemi = someone else’s pen

So if you want to express belonging to another person, you need a possessive structure like başkasının or başka birinin.

No. Turkish does not mark gender the way English does.

The 3rd-person possessive ending can mean:

• his
• her
• its

So kalemi / kalemini does not tell you the gender of the owner. In this sentence, it simply refers back to başkası = someone else.

Yes. It shows that the pen is a specific direct object.

Turkish often marks specific objects with the accusative. In this sentence, someone else’s pen is a definite, identifiable thing, so kalemini is the expected form.

That is one reason Turkish learners often notice that direct objects are marked more clearly than in English.