Kıdem tazminatı fesihten sonra son bordroya eklendi.

Usually, no. In this sentence, kıdem tazminatı is a noun compound, not an accusative noun.

It is built like this:

• kıdem = seniority, length of service
• tazminat = compensation
• tazminatı = the second noun takes the compound ending

This pattern is very common in Turkish:

• çocuk kitabı = children’s book
• otobüs durağı = bus stop
• kıdem tazminatı = severance pay

So the -ı here is part of the fixed compound. If it were accusative, you would normally see an extra accusative marker:

• kıdem tazminatını = the severance pay (as a definite direct object)

In your sentence, kıdem tazminatı is the subject of the verb eklendi.

Fesihten is in the ablative case: -den / -dan / -ten / -tan.

Here:

• fesih = termination, rescission
• fesihten = from the termination / after the termination

With sonra, Turkish normally uses the ablative:

• toplantıdan sonra = after the meeting
• işten sonra = after work
• fesihten sonra = after the termination

So X-den sonra is the standard pattern for after X.

Because the verb eklenmek takes the dative case for the thing something is added to.

Compare:

• bir şeyi bir şeye eklemek = to add something to something
• bir şey bir şeye eklendi = something was added to something

So here:

• bordro = payroll / payslip
• bordroya = to the payroll / to the payslip

That is why the sentence uses son bordroya eklendi = was added to the final payroll/payslip.

Because eklendi is the passive form.

• ekledi = he/she/it added
• eklendi = it was added

The active verb is eklemek = to add.
The passive form is eklenmek = to be added.

So:

• Muhasebe kıdem tazminatını son bordroya ekledi.
  = Accounting added the severance pay to the final payroll.

• Kıdem tazminatı son bordroya eklendi.
  = The severance pay was added to the final payroll.

In your sentence, the focus is on the result, not on who did it.

It is the simple past with -di.

Structure:

• ekle-n-di
• ekle- = add
• -n- = passive
• -di = past tense

So eklendi means was added or got added.

This tense usually presents the action as a completed fact.

Yes. The sentence is very natural.

A rough breakdown is:

• Kıdem tazminatı = subject
• fesihten sonra = time expression
• son bordroya = destination/target
• eklendi = verb

Turkish word order is flexible, but the verb usually comes at the end in neutral written language.

You could also say:

• Fesihten sonra kıdem tazminatı son bordroya eklendi.

That version puts slightly more focus on the time phrase first. Both are natural.

Because Turkish does not have articles like English a and the.

Whether something is definite or indefinite is understood from:

• context
• word order
• case marking
• modifiers such as son = final/last

So son bordro already strongly suggests a specific payroll/payslip: the final payroll.

Likewise, kıdem tazminatı is understood as the relevant severance pay in that context.

It can mean either, depending on context.

In workplace Turkish, bordro can refer to:

• a payroll record
• a pay statement
• a payslip

So son bordro may be translated as:

• the final payroll
• the final payslip
• the last payroll record

The best English choice depends on the situation and the translation style.

Not really. Fesih is a formal/legal/business word.

You are likely to see it in:

• HR documents
• contracts
• legal writing
• official company communication

In everyday speech, people might say something more conversational, depending on the situation, such as:

• işten çıkarma = dismissal
• ayrılma = leaving
• sözleşmenin bitmesi = the contract ending

So this sentence sounds like business or legal Turkish, not casual conversation.

Son is just an adjective here, meaning last or final.

So:

• son bordro = final payroll / last payslip

Turkish adjectives do not agree with nouns in number or case. The case ending goes on the noun, not the adjective:

• son bordro
• son bordroya
• son bordrodan

So only bordro changes, not son.

Yes, in some contexts.

Because eklendi is passive, English may render it as:

• was added
• got added

Was added is usually better for formal or business translation.
Got added sounds more conversational.

Since your Turkish sentence is formal in tone, was added is normally the best match.