Mahkeme faydalı modeli ve patent ihlalini ayrı inceliyor.

Yes:

• Mahkeme = the court / a court
• faydalı modeli = the utility model
• ve = and
• patent ihlalini = the patent infringement
• ayrı = separately
• inceliyor = is examining / examines

A very literal word order would be:

• The court the utility model and the patent infringement separately examines.

That sounds unnatural in English, but it matches normal Turkish structure.

Because they are direct objects, and in this sentence they are understood as specific/definite ones.

Turkish often marks a specific direct object with the accusative ending.

• faydalı model → faydalı modeli
• patent ihlali → patent ihlalini

So the sentence is not talking about just any utility model or any patent infringement, but about particular ones already known in context.

Because patent ihlali is already a noun compound.

In Turkish, many compounds are built like this:

• patent ihlali = patent infringement

Here, ihlali already contains the compound ending.
When you then add the accusative, Turkish uses a buffer n, not y:

• patent ihlali
  • -ni → patent ihlalini

So:

• ihlaliyi = not correct here
• ihlalini = correct

A simple way to remember it:

• after a plain vowel-final noun, Turkish often uses y
• after this kind of possessed/compound form, Turkish uses n

In standard Turkish, both coordinated nouns normally take the case ending if both are direct objects.

So this is natural:

• faydalı modeli ve patent ihlalini

Not:

• faydalı model ve patent ihlalini

Since both things are being examined, both are marked as objects.

It is structurally an adjective + noun phrase:

• faydalı = useful / beneficial
• model = model

But in legal and intellectual-property language, faydalı model is also a set term meaning utility model.

So in this sentence, it is best to understand it as one legal term, not as a casual phrase meaning a useful model.

Because Turkish usually prefers Subject–Object–Verb order.

Here the order is:

• Mahkeme = subject
• faydalı modeli ve patent ihlalini = object(s)
• ayrı = adverb
• inceliyor = verb

So putting the verb at the end is completely normal Turkish sentence structure.

İnceliyor is the -yor form, often called the present continuous.

Its basic meaning is:

• is examining

But in real Turkish, this form is also often used for:

• current processes
• ongoing official actions
• what is happening in a case or situation right now

So in English, it may be translated either as:

• is examining
• examines

depending on context.

By contrast, inceler more often sounds like:

• a habitual action
• a general rule
• examines / will examine in a more timeless or formal sense

Here ayrı means separately.

It tells you that the court is not treating the two issues as one combined matter. Instead, it is examining:

• the utility model
• and the patent infringement

separately, one apart from the other.

So ayrı is functioning like an adverb in this sentence.

Yes. Ayrı ayrı is also very common and often sounds a bit more explicit:

• Mahkeme faydalı modeli ve patent ihlalini ayrı ayrı inceliyor.

That would mean essentially the same thing:
The court is examining the utility model and the patent infringement separately.

In your sentence, ayrı alone is already fine, especially in a formal or written style.

Because Turkish has no definite article like English the.

So mahkeme can mean:

• a court
• the court

The exact meaning depends on context.

In a sentence like this, especially in legal context, Mahkeme is naturally understood as the court.