Во-вторых, нам нужно больше времени.

It is a discourse marker meaning secondly or in the second place. It does not describe the action itself; it helps organize the speaker’s argument or list of points.

So:

• Во-первых, ... = First, ...
• Во-вторых, ... = Second, ...
• В-третьих, ... = Third, ...

In this sentence, во-вторых shows that this is the speaker’s second reason or second point.

Во-вторых is a fixed adverbial expression. You usually learn it as one chunk.

A few things are happening here:

• во- is part of the standard pattern in these list words: во-первых, во-вторых
• -ых comes from an older case form that survives in this expression
• the whole phrase functions as an adverb, not as a normal noun or adjective phrase

So even if it looks strange at first, the best approach is to memorize:

• во-первых
• во-вторых
• в-третьих

You normally would not replace it with во второй in this meaning.

Because во-вторых is an introductory word/phrase that structures the sentence. In Russian, such expressions are usually separated by commas.

Examples:

• Во-первых, это дорого.
• Во-вторых, нам нужно больше времени.
• Наконец, всё готово.

The comma shows that во-вторых is not a core part of the clause; it is a comment on how the sentence fits into the overall argument.

Because нам is the dative case of мы (we).

The sentence is built like this:

• нам = to us / for us
• нужно = is necessary / is needed
• больше времени = more time

A very literal version is:

To us, more time is necessary.

Russian often uses this kind of structure instead of saying we need with a personal subject.

Forms of мы:

• мы = we
• нас = us
• нам = to us

Here, the dative is required by нужно.

Here нужно means needed / necessary in an impersonal construction.

The pattern is very common:

• мне нужно... = I need...
• тебе нужно... = you need...
• нам нужно... = we need...

Grammatically, Russian is not saying we need in the same way English does. It is saying something more like:

• to me, it is necessary
• to us, it is necessary

That is why you do not see a normal subject like мы.

Because impersonal predicates like нужно, можно, нельзя often appear in a fixed neuter singular form.

Compare:

• Мне нужно идти. = I need to go.
• Ему нужно время. = He needs time.
• Нам нужно больше времени. = We need more time.

You do not change нужно to match нам. The sentence is impersonal, so нужно stays the same.

Because after больше (more), Russian normally uses the genitive case.

So:

• время = nominative
• времени = genitive

That is why you get:

• больше времени = more time
• больше денег = more money
• больше людей = more people

This is a very common pattern. After quantity words like больше and меньше, the following noun is usually in the genitive.

It is the genitive singular of время.

The noun время is irregular, so its forms are worth learning:

• время = nominative singular
• времени = genitive singular
• времени = dative singular
• время = accusative singular
• временем = instrumental singular
• о времени = prepositional singular

In this sentence, it is genitive because of больше.

Yes. Нам надо больше времени is perfectly natural and means almost the same thing.

A rough comparison:

• нужно = needed / necessary
• надо = need to / have to / necessary

In many everyday sentences, they are interchangeable:

• Мне нужно уйти.
• Мне надо уйти.

Both are common. In your sentence:

• Нам нужно больше времени
• Нам надо больше времени

Both sound normal. Нужно can feel slightly more neutral or formal in some contexts, but the difference is often small.

Yes, Russian word order is flexible, though different orders can slightly change emphasis.

The neutral order here is:

• Нам нужно больше времени.

Other possible orders:

• Больше времени нам нужно.
  This emphasizes more time.
• Нужно нам больше времени.
  Possible, but less neutral and more marked.
• Нам больше времени нужно.
  Also possible, with a slightly different rhythm/emphasis.

For most learners, Нам нужно больше времени is the safest and most natural choice.

Yes, if the context already makes it clear who needs more time.

• Нужно больше времени. = More time is needed. / We need more time. / It takes more time.

Without нам, the sentence becomes more general or less explicit about who needs it.

With нам, the sentence clearly means we need more time.

Very literally, it is something like:

Secondly, to us it-is-necessary more of-time.

That sounds unnatural in English, but it helps show the Russian structure:

• Во-вторых = secondly
• нам = to us
• нужно = is necessary / is needed
• больше времени = more time

A natural English translation is simply Secondly, we need more time.

The main stresses are:

• во-вторы́х
• нам
• ну́жно
• бо́льше
• вре́мени

So the whole sentence sounds roughly like:

во-вторы́х, нам ну́жно бо́льше вре́мени

This is useful because stress in Russian is unpredictable and can affect pronunciation a lot.