Между прочим, если письмо написано ясно и без лишних слов, получатель отвечает быстрее.

In this sentence, между прочим is an idiomatic parenthetical phrase meaning something like by the way, incidentally, or as a side note.

It is not being used literally as between other things here. Native speakers often use между прочим to introduce an extra comment that feels relevant but slightly aside from the main point.

So the sentence structure is roughly:

By the way, if a letter is written clearly and without unnecessary words, the recipient replies faster.

Because между прочим is a parenthetical expression. In Russian, parenthetical words and phrases are often separated by commas.

So:

• Между прочим, ... = By the way, ...

The comma shows that this phrase is not a core part of the clause structure.

That comma separates the if-clause from the main clause.

• если письмо написано ясно и без лишних слов = if the letter is written clearly and without unnecessary words
• получатель отвечает быстрее = the recipient replies faster

In Russian, clauses introduced by если are normally separated by a comma from the main clause.

Если means if and introduces a condition.

The sentence is talking about a general condition:

• If a letter is written clearly... the recipient replies faster.

If you used когда, that would mean when, which suggests something more definite or habitual in a different way. Here the speaker is expressing a cause-and-effect condition, so если is the natural choice.

Письмо написано means the letter is written or the letter has been written. This is a short-form passive construction.

Breakdown:

• письмо = letter
• написано = short passive participle of написать

So письмо написано ясно means the letter is written clearly.

Why not the others?

• письмо пишет would mean the letter writes, which makes no sense.
• написанное письмо means a written letter, which is an adjective-like phrase, not the predicate of the sentence.

Here Russian wants a predicate: the letter is written clearly.

Because it agrees with письмо, which is a neuter singular noun.

Russian short-form passive participles agree in gender and number with the noun they describe:

• письмо написано — neuter singular
• статья написана — feminine singular
• документ написан — masculine singular
• письма написаны — plural

So написано matches письмо.

Here ясно functions like an adverb meaning clearly.

It describes how the letter is written:

• написано ясно = written clearly

This is very common in Russian. Forms in -о often work adverbially:

• говорить ясно = to speak clearly
• писать кратко = to write briefly
• объяснять просто = to explain simply

Even though ясно can also appear in other uses, here it is best understood as an adverb.

Because the preposition без requires the genitive case.

Base forms:

• лишние слова = unnecessary words
• after без → без лишних слов = without unnecessary words

So both words change:

• лишние → лишних
• слова → слов

This phrase means something like:

• without unnecessary words
• without extra wording
• without needless verbiage

Russian has no articles like a, an, or the.

So письмо can mean:

• a letter
• the letter

and получатель can mean:

• a recipient
• the recipient

The exact meaning depends on context. In this sentence, the meaning is general, so English usually uses:

• if a letter is written clearly ... the recipient replies faster or
• if a letter is written clearly ... a recipient replies faster

Often English may also rephrase it more naturally as a general truth.

Because отвечает is imperfective, and it is used here for a general habitual result.

The sentence is not about one single future reply. It means something like:

• In general, the recipient replies faster.

If you used ответит, that would sound more like a one-time completed future action:

• the recipient will reply faster

That is less natural for this kind of general statement.

Быстрее is the comparative form meaning faster.

Russian usually prefers simple comparative forms like:

• быстрее = faster
• лучше = better
• короче = shorter

So:

• получатель отвечает быстрее = the recipient replies faster

Более быстро is grammatically possible in some contexts, but it is less natural here. The simple comparative быстрее is the normal choice.

The basic meaning would stay the same if you changed the word order a bit, but the original order sounds natural and neutral.

Original:

• Между прочим, если письмо написано ясно и без лишних слов, получатель отвечает быстрее.

Possible variations:

• Если письмо написано ясно и без лишних слов, получатель отвечает быстрее.
• Получатель отвечает быстрее, если письмо написано ясно и без лишних слов.

Russian word order is more flexible than English, but it still affects emphasis and style. The given version sounds like a normal explanatory statement with между прочим added at the beginning.

Russian can leave that unstated when it is obvious from context.

Here отвечает simply means replies / responds. Since the sentence is about a letter, the listener naturally understands that the recipient replies to the letter.

English can do the same:

• The recipient replies faster.

So no explicit object is necessary.