Nonostante la batteria esausta occupi poco spazio, dobbiamo smaltirla.

Because nonostante introduces a concessive idea (although / despite the fact that), and in standard Italian that often leads to the subjunctive when a full clause follows.

• occupa = indicative
• occupi = present subjunctive

So:

• Nonostante la batteria esausta occupi poco spazio... = Although the dead battery takes up little space...

A learner will often notice this because in English we do not change the verb form in the same way.

Not always in every possible structure, but in sentences like this one, where nonostante is followed by a clause with its own verb, the subjunctive is the normal standard choice.

Compare:

• nonostante la pioggia = despite the rain
  
  • here there is no verb, so no subjunctive issue
• nonostante piova = although it is raining
  
  • here there is a verb, so the subjunctive is used

So in your sentence:

• nonostante la batteria esausta occupi poco spazio

the clause after nonostante has a verb, so occupi is in the subjunctive.

Here esausta means something like exhausted, used up, or dead. With a battery, the natural English translation is usually dead battery or drained battery.

You may also hear:

• batteria scarica = flat/dead battery
• batteria esausta = often used in more formal, technical, or recycling/disposal contexts

So:

• La batteria è scarica = the battery has no charge
• Una batteria esausta often suggests a battery that is spent and should be disposed of properly

In this sentence, esausta fits especially well because the second part talks about smaltirla (disposing of it).

In Italian, many adjectives commonly come after the noun, especially when they describe a factual quality.

So:

• la batteria esausta = the dead/used-up battery

This is the normal, neutral order.

If an adjective comes before the noun, it often changes tone or emphasis, but with esausta, post-noun position is the natural choice here.

Because the sentence is referring to a specific battery already identifiable in context, so Italian uses the definite article:

• la batteria esausta

Italian uses articles more often than English does. English might sometimes say dead battery in a general way, but Italian often prefers the article when talking about a concrete item under discussion.

Occupare spazio means to take up space or to occupy space.

So:

• occupa poco spazio = it takes up little space

This is a very common expression in Italian:

• Questo mobile occupa troppo spazio. = This piece of furniture takes up too much space.
• Il file occupa poco spazio. = The file takes up little space.

Because poco can directly modify a noun as a quantity word:

• poco spazio = little space
• poca acqua = little water
• poco tempo = little time

You do not normally need di here.

Also notice agreement:

• spazio is masculine singular
• so the form is poco

Compare:

• poco spazio
• poca energia

Both are correct.

• dobbiamo smaltire la batteria = we must dispose of the battery
• dobbiamo smaltirla = we must dispose of it

In your sentence, Italian uses the direct object pronoun la to avoid repeating la batteria.

The pronoun is attached to the infinitive:

• smaltire + la → smaltirla

This is very common in Italian.

Other examples:

• voglio comprarlo = I want to buy it
• possiamo usarla = we can use it
• devo buttarli = I must throw them away

Because the pronoun refers to la batteria, which is:

• feminine
• singular

So the correct direct object pronoun is:

• la = it (feminine singular)

Compare:

• il libro → lo
• la batteria → la
• le pile → le

So:

• dobbiamo smaltirla = we must dispose of it

Here smaltire means to dispose of properly, especially waste, used materials, or potentially harmful items.

With a battery, it does not just mean to throw away casually. It suggests proper disposal, recycling, or waste processing.

So depending on context, it could be translated as:

• dispose of it
• get rid of it properly
• recycle it / send it for disposal

This is why smaltire is a very appropriate verb for batteria esausta.

Grammatically, yes, but it changes the meaning and tone.

• buttarla via = throw it away
• smaltirla = dispose of it properly

For a battery, smaltirla is much better because batteries should not simply be thrown out with normal trash. Italian often uses smaltire for environmentally responsible disposal.

So in this sentence, smaltirla is the best choice.

Because Italian often expresses although / even though with a concessive clause introduced by nonostante, and that clause can come before the main clause.

Structure:

• Nonostante + clause, main clause

So:

• Nonostante la batteria esausta occupi poco spazio, dobbiamo smaltirla.

This is very natural Italian and corresponds to English:

• Although the dead battery takes up little space, we must dispose of it.

Italian word order here is not strange; it is a standard way to present the contrast first and the main point after.

Yes, it sounds fairly neutral-to-formal, especially because of:

• esausta
• smaltirla
• the use of the subjunctive after nonostante

A more everyday version might be something like:

• Anche se la batteria scarica occupa poco spazio, dobbiamo buttarla via correttamente.

But your original sentence is perfectly natural, especially in written Italian, instructions, environmental information, or educational material.