Se dobbiamo traslocare anche il tavolo, ci serve un secondo furgone.

Because this is a normal, real condition: If we have to...

After se meaning if, Italian usually uses the indicative for real or likely situations:

• Se piove, restiamo a casa. = If it rains, we stay home.
• Se dobbiamo traslocare anche il tavolo, ci serve... = If we also have to move the table, we need...

The subjunctive is generally not used after se in this kind of sentence.

Dobbiamo means we must / we have to.

So dobbiamo traslocare means we have to move.

A useful detail: traslocare often means to move house / relocate, but in everyday usage it can also be used for moving belongings during a move, as in this sentence with il tavolo. So here it means something like:

• we have to move the table as part of the move

In some contexts, learners may more often see verbs like spostare or portare via for moving an object, but this sentence is natural in the context of a house move.

Yes, in modern everyday Italian it can.

Traditionally, traslocare is often taught first as an intransitive verb:

• Traslochiamo domani. = We’re moving tomorrow.

But in real usage, especially when talking about furniture and belongings, Italians also use it transitively:

• Dobbiamo traslocare i mobili. = We have to move the furniture.

So traslocare il tavolo is understandable and natural in context.

Here anche il tavolo means the table too / the table as well.

Placing anche before il tavolo makes it clear that the table is the extra thing being added:

• Se dobbiamo traslocare anche il tavolo...
  = If we have to move the table too...

This is different from:

• Se dobbiamo anche traslocare il tavolo...

That version can also be possible, but it puts the focus slightly more on the action also having to move, rather than specifically on the table as the extra item.

Ci here means to us.

So:

• ci serve = is needed by us / we need

Italian often expresses to need with servire in this structure:

• Mi serve = I need
• Ti serve = you need
• Ci serve = we need

Literally, ci serve un secondo furgone is something like:

• A second van is necessary for us

But in natural English, that is just:

• We need a second van

Because the subject is un secondo furgone, which is singular.

With servire, the verb agrees with the thing needed, not with the person who needs it:

• Ci serve un furgone. = We need a van.
• Ci servono due furgoni. = We need two vans.

So in your sentence:

• un secondo furgone = singular
• therefore serve = singular

It certainly can.

Both are natural:

• Ci serve un secondo furgone.
• Abbiamo bisogno di un secondo furgone.

The difference is mostly stylistic:

• ci serve is often more direct and conversational
• abbiamo bisogno di is a bit fuller and sometimes slightly more formal or explicit

So the sentence could be rephrased as:

• Se dobbiamo traslocare anche il tavolo, abbiamo bisogno di un secondo furgone.

Same basic meaning.

Yes. Un secondo furgone means a second van, and in this context that naturally means another van in addition to the first one.

So it implies there is already one van, but that one is not enough.

Compare:

• un furgone = a van
• un secondo furgone = a second van / another van

Yes, and that is very common in Italian.

Even if the move is in the future, Italian often uses the present tense when the future meaning is clear from context:

• Se dobbiamo traslocare anche il tavolo, ci serve un secondo furgone.

This can refer to a present decision about a future move, just like English often says:

• If we have to move the table too, we need a second van.

Italian does not need a future tense here.

Yes, that is grammatically possible.

• Se dobbiamo... = If we have to...
• Se dovremo... = If we will have to...

In many everyday situations, Italian prefers the present tense dobbiamo where English might also simply use the present or have to. Using dovremo is possible, but it can sound a bit more explicitly future-oriented or a bit heavier in tone.

In ordinary conversation, Se dobbiamo... is very natural.

Because Italian usually leaves subject pronouns out when they are clear from the verb ending.

• dobbiamo already means we have to
• so there is no need to say noi

You could say:

• Se noi dobbiamo traslocare anche il tavolo...

But that would usually add emphasis, contrast, or special focus. Normally, just dobbiamo is enough.

The basic structure is:

• ci = to us
• serve = is needed
• un secondo furgone = a second van

So literally it is close to:

• To us is needed a second van

But in natural English, that becomes:

• We need a second van

Italian often uses this pattern with servire:

• Mi serve una penna. = I need a pen.
• Ci serve più tempo. = We need more time.

Yes, and that may even feel more straightforward to many learners.

• spostare = to move something from one place to another
• traslocare = to move house / move belongings during a move

So:

• Se dobbiamo spostare anche il tavolo...
  can sound more like simply moving the table

while

• Se dobbiamo traslocare anche il tavolo...
  fits the idea of moving it as part of a larger relocation

Both can work, but they are not always identical in nuance.