Из-за невнимательности я написал адрес с ошибкой.

Here из-за means because of.

So:

• из-за невнимательности = because of inattentiveness / due to carelessness

It is written with a hyphen because из-за is a fixed preposition. Historically it comes from из + за, but in this meaning you should learn it as one unit.

A useful extra note: из-за can also mean from behind in other contexts:

• из-за дома = from behind the house

So this preposition has two common meanings:

• because of
• from behind

Only the context tells you which one it has.

Because из-за requires the genitive case.

The base noun is:

• невнимательность = inattentiveness, carelessness

Its genitive singular form is:

• невнимательности

So:

• из-за невнимательности = because of inattentiveness

This is a very common pattern:

• из-за дождя = because of the rain
• из-за ошибки = because of the mistake
• из-за усталости = because of tiredness

Yes, absolutely. По невнимательности is very natural here.

Compare them:

• из-за невнимательности = because of inattentiveness
• по невнимательности = through inattentiveness / by mistake / out of carelessness

In many situations they are very close in meaning.
However, по невнимательности often sounds a little more like accidentally, through carelessness, while из-за невнимательности simply states the cause.

So this sentence could also be:

• По невнимательности я написал адрес с ошибкой.

That sounds perfectly normal.

Because написал is perfective, while писал is imperfective.

• писать / писал = to write / was writing, wrote in a process-oriented sense
• написать / написал = to write, finish writing, complete the act

In this sentence, the speaker is talking about a completed result: the address ended up written, and it contained an error. That is why написал is the natural choice.

Compare:

• Я писал адрес. = I was writing the address / I wrote the address (focus on process, background, or repeated action depending on context)
• Я написал адрес. = I wrote down the address / I finished writing the address

Because the mistake is part of the final result, the perfective verb fits especially well.

Here адрес is in the accusative case, because it is the direct object of написал.

The dictionary form is nominative singular:

• адрес

For many masculine inanimate nouns, the accusative singular is identical to the nominative singular. So:

• nominative: адрес
• accusative: адрес

That is why the form does not change.

Compare with another masculine inanimate noun:

• Я вижу стол. = I see the table.

But with an animate masculine noun, accusative usually matches genitive:

• Я вижу брата. = I see my brother.

Because this is the expression с ошибкой, which means with a mistake / containing an error.

The preposition с here means with, and in this meaning it normally takes the instrumental case:

• ошибка → ошибкой (instrumental singular)

So:

• адрес с ошибкой = an address with an error

You would use ошибку (accusative) in a different structure, for example:

• Я сделал ошибку. = I made a mistake.
• Я допустил ошибку. = I made/committed an error.

But in this sentence, the idea is not I made a mistake as a separate object. The idea is that the address was written in an incorrect form, so Russian uses с ошибкой.

It can be understood as connected to the result of the action: the address was written with an error.

In practice, English speakers often think of it as either:

• I wrote the address incorrectly
• I wrote the address with a mistake
• I wrote down the address containing an error

Russian often expresses this idea through a noun phrase like с ошибкой instead of an adverb.

So yes, grammatically it feels close to адрес (an address with an error), but semantically it also describes the whole writing event.

Yes. Russian word order is flexible, and the sentence can be rearranged depending on emphasis.

Neutral order:

• Из-за невнимательности я написал адрес с ошибкой.

Other possible orders:

• Я написал адрес с ошибкой из-за невнимательности.
• Адрес я написал с ошибкой из-за невнимательности.
• С ошибкой я написал адрес из-за невнимательности. (possible, but more marked)

The original version is natural because it puts the cause first:

• Из-за невнимательности = because of carelessness

That sets up the explanation before the main action.

It is close, but not always exactly the same.

Невнимательность literally means inattention / lack of attentiveness. Depending on context, it can also be translated as:

• carelessness
• inattentiveness
• not paying attention

In this sentence, the idea is that the speaker was not attentive enough and therefore made an error. So English might naturally say:

• because of carelessness
• because I wasn’t paying attention
• through inattention

All of those are reasonable translations of the underlying Russian idea.

In modern Russian, адрес usually means an address in the location/contact sense:

• street address
• postal address
• sometimes email/web address, depending on context

It does not usually mean a speech to an audience the way English address can. For that meaning, Russian uses different words.

So in this sentence, адрес is clearly something written down incorrectly, such as a mailing or street address.

Yes. The original sentence is correct and natural, but everyday Russian might also use slightly different phrasing, for example:

• По невнимательности я написал адрес с ошибкой.
• Я по невнимательности написал адрес с ошибкой.
• Я по ошибке неправильно написал адрес.

These are all natural, but the meanings are not perfectly identical:

• по невнимательности = through inattentiveness
• по ошибке = by mistake
• неправильно написал = wrote incorrectly

Your original sentence is fully good Russian; these are just common alternatives.