Signora, in una mail formale scrivo il Suo nome con la maiuscola e non uso abbreviazioni o lettere minuscole a caso.

Signora is a direct form of address, like Madam in English. The speaker is addressing the person directly, so Italian usually separates it with a comma.

• Signora, ... = Madam, ...
• Marco, vieni qui. = Marco, come here.

That comma marks the vocative, meaning the person being spoken to.

Both are possible in modern Italian. Mail and email / e-mail are all commonly used.

A few notes:

• una mail is very common in everyday and business Italian.
• un'email is also correct and very common.
• mail is treated as feminine here, so you get una mail.
• formale means formal, so una mail formale means a formal email.

So this is a natural modern phrasing, not a mistake.

The present tense in Italian often expresses a general habit or rule, not just something happening right now.

So scrivo here means something like:

• I write
• when I write
• in formal emails, I write...

It is describing the speaker's usual practice. Italian often uses the simple present for this kind of statement.

The capital letter in Suo shows formal respect. In formal Italian, possessives and pronouns referring to the person you are addressing may be capitalized:

• Lei
• La
• Le
• Suo / Sua / Suoi / Sue

So il Suo nome means your name in a respectful, formal way.

This capitalization is especially associated with formal letters, emails, and polite business communication. Today it is still used, though some people consider it a bit traditional or extra-formal.

In Italian, possessives are usually used with a definite article:

• il mio libro
• la tua macchina
• il Suo nome

So il Suo nome is normal Italian grammar.

English often says your name without an article, but Italian usually needs one.

A common exception is with close family members in the singular:

• mia madre
• tuo fratello

But nome is not one of those exceptions, so il Suo nome is correct.

No. Suo agrees grammatically with nome, not with the person who owns the name.

• nome is masculine singular
• so the possessive is Suo

Compare:

• il Suo nome = your name
• la Sua email = your email
• i Suoi documenti = your documents
• le Sue richieste = your requests

The person addressed may be male or female; the possessive changes according to the noun, not the owner.

It literally means with the capital letter or capitalized.

In this sentence, it means the name is written with proper capitalization, especially the initial capital letter.

• maiuscola = uppercase / capital letter
• lettera maiuscola = capital letter

So scrivo il Suo nome con la maiuscola means the speaker writes the person's name using the correct capital letter(s), instead of writing it in lowercase.

They are being used a little differently.

• con la maiuscola is a set phrase meaning with a capital letter / capitalized
• lettere minuscole literally means lowercase letters

So:

• la maiuscola = the use of uppercase / a capital letter
• lettere minuscole = lowercase letters

Italian often uses maiuscola and minuscola this way when talking about capitalization.

It means I do not use abbreviations.

There is no article because the speaker is talking about abbreviations in a general sense, not specific ones.

Compare:

• Non uso abbreviazioni. = I don't use abbreviations.
• Non uso le abbreviazioni che mi hai mandato. = I don't use the abbreviations you sent me.

This is very common in Italian: plural nouns used generically often appear without an article.

A caso means randomly, arbitrarily, or without a clear rule.

So lettere minuscole a caso means lowercase letters used randomly, for no good reason, or in the wrong places.

Examples:

• scegliere a caso = to choose at random
• parlare a caso = to speak at random / without thinking
• mettere maiuscole a caso = to put capital letters in random places

Here it criticizes inconsistent writing style.

Both are possible, but they are slightly different in tone.

• non ... o ... is perfectly normal and means I do not use abbreviations or random lowercase letters
• non ... né ... is a bit more formal or emphatic: I use neither abbreviations nor random lowercase letters

So the sentence as written is completely correct and natural.
Using né would make it sound a little more structured or rhetorical.

Yes, in this sentence it is feminine: una mail.

That is very common in Italian. You will often hear:

• una mail
• la mail
• le mail

With email, usage can vary a bit, but una email is also very common.

Not strictly required in every context, but it is still a recognized and polite convention in formal writing.

You may see both:

• La ringrazio per il Suo aiuto.
• La ringrazio per il suo aiuto.

Both can be acceptable, depending on house style, company style, and personal preference.

In very formal or traditional correspondence, capitalization like Suo often appears to show respect. In more modern business Italian, many people now prefer lowercase, except perhaps for La / Le / Lei in some contexts.

So in this sentence, the capital Suo is formal and polite, not wrong or strange.

Italian usually drops subject pronouns when they are not needed, because the verb ending already shows the person.

• scrivo = I write
• uso = I use

So io would only be added for emphasis or contrast:

• Io scrivo il Suo nome con la maiuscola, non altri.

Without emphasis, Italian normally leaves io out.