Игла дротика новая.

Because дротика is the genitive singular form of дротик.

Here it shows possession or close relationship:

• игла дротика = the needle/point of the dart or the dart’s needle/point

This is a very common Russian pattern:

• крыша дома = the roof of the house
• дверь машины = the car’s door
• игла дротика = the dart’s point

So игла is the main noun, and дротика tells you whose needle/point it is.

Because игла is in the nominative singular, which is the usual form for the subject.

The structure is:

• Игла = subject
• дротика = dependent noun in the genitive, modifying игла
• новая = predicate adjective describing игла

So the sentence is basically:

• Игла дротика новая = The dart’s point is new

The thing being described as new is игла, not дротик.

Because it agrees with игла, and игла is a feminine noun.

In Russian, adjectives must agree with the noun they describe in:

• gender
• number
• case

Since игла is:

• feminine
• singular
• nominative

the adjective must also be:

• feminine
• singular
• nominative

That gives новая.

Compare:

• новый дротик = a new dart
• новая игла = a new needle/point
• новое копьё = a new spear
• новые дротики = new darts

In Russian, the verb to be is normally omitted in the present tense.

So where English says:

• The dart’s point is new

Russian simply says:

• Игла дротика новая.

This is completely normal.

Compare:

• Дом большой. = The house is big.
• Книга интересная. = The book is interesting.
• Игла дротика новая. = The dart’s point is new.

If you talk about the past or future, a form of быть appears:

• Игла дротика была новой. = The dart’s point was new.
• Игла дротика будет новой. = The dart’s point will be new.

Because of agreement.

• игла is feminine singular nominative
• новая is also feminine singular nominative

But дротика is masculine genitive singular, so новая cannot agree with it.

If the adjective described дротика, it would need a different form, depending on the structure.

So the matching endings tell you that:

• игла ... новая

belong together grammatically.

Yes. Russian word order is more flexible than English word order.

This sentence:

• Игла дротика новая.

could also be rearranged in some contexts, for example:

• Новая игла дротика. = the new point of the dart
• Игла новая. = The point is new.
• У дротика новая игла. = The dart has a new point.

But the exact emphasis changes.

In Игла дротика новая, the sentence sounds like a statement about the point: it is new.

Russian word order often helps show:

• topic vs. new information
• emphasis
• style

Russian usually does not show possession with something like English ’s.

Instead, it often uses:

• a noun in the genitive case
• or another possessive construction

So English:

• the dart’s point

often becomes Russian:

• игла дротика

Literally, that is more like:

• the point of the dart

This is one of the most common ways Russian expresses possession.

It could mean either, depending on context.

Russian has no articles like a and the. So:

• Игла дротика новая.

does not itself tell you whether the noun is definite or indefinite.

Context decides:

• If you have already been talking about a specific dart, it may mean the dart’s point is new.
• In a more general or first-mention context, it could feel more like a dart’s point is new.

In actual translation, English usually needs a or the, but Russian does not.

In modern Russian, the full adjective form is very commonly used in predicate position:

• Игла дротика новая.

That is normal and neutral.

Russian also has short-form adjectives, and for новый the feminine short form is нова:

• Игла дротика нова.

But this sounds more literary, formal, or stylistically marked. For everyday speech, новая is much more natural here.

So for learners, the safest choice is:

• use новая in this kind of sentence

Literally, игла means needle, but it can also refer to a sharp pointed part of something.

So in context, it can mean something like:

• needle
• point
• tip

A learner may notice that English would often prefer tip or point rather than needle. That is a vocabulary issue rather than a grammar issue.

Grammatically, the sentence still works the same way:

• игла = the pointed part
• дротика = of the dart
• новая = new

The pattern is:

• [Noun in nominative] + [dependent noun in genitive] + [predicate adjective]

In this sentence:

• Игла = nominative subject
• дротика = genitive modifier
• новая = predicate adjective

So you can think of it as:

• The point of the dart is new

This is a very useful Russian pattern, and you will see it often.