Signora, il suo ombrello è vicino alla porta.

Signora is a form of direct address, like Madam, Ma’am, or sometimes Mrs. in English. The speaker is talking to the woman, so Italian sets that off with a comma:

Signora, il suo ombrello è vicino alla porta.

That comma works like the comma in English direct address: Ma’am, your umbrella is near the door.

It is capitalized here mainly because it is the first word of the sentence.

That is a very common question. Suo can mean his, her, its, or your in the formal sense.

Italian uses Lei as the formal word for you, but grammatically Lei takes third-person forms. Because of that, the possessive is also third-person:

• il tuo ombrello = your umbrella (informal)
• il suo ombrello = your umbrella (formal)

So in this sentence, because the speaker says Signora, we understand that suo means your.

In very formal writing, you may also see it capitalized as Suo, but lowercase suo is very common today.

In Italian, possessives usually go with a definite article:

• il mio libro
• la tua borsa
• il suo ombrello

So Italian normally says the your umbrella, the my book, and so on, even though English does not.

A famous exception is with many singular close-family words when they are not modified:

• mia madre
• tuo fratello
• sua sorella

But ombrello is not a family word, so the article stays: il suo ombrello.

If ombrello appeared by itself, you would say:

l'ombrello

because it starts with a vowel.

But when a possessive comes before the noun, Italian normally uses the full article il with masculine singular nouns:

• il mio amico
• il suo ombrello

So the pattern is:

• l'ombrello = the umbrella
• il suo ombrello = your/his/her umbrella

In other words, the possessive changes the article pattern.

Because the possessive agrees with the thing possessed, not with the owner.

The noun here is ombrello, which is masculine singular, so the possessive must also be masculine singular:

• il suo ombrello = umbrella is masculine singular
• la sua borsa = bag is feminine singular

It does not matter that Signora refers to a woman. The form depends on ombrello, not on the person who owns it.

The accent shows that è is the verb is.

This matters because e without an accent means and.

So:

• è = is
• e = and

The accent helps both spelling and meaning.

Because vicino normally goes with the preposition a when it means near:

• vicino a = near / close to

Then a + la combines into alla:

• a + la = alla

So:

• vicino alla porta = near the door

In standard Italian, vicino la porta is not the usual form here. The expected pattern is vicino a + noun.

Here vicino matches ombrello, which is masculine singular.

So the pattern is:

• l'ombrello è vicino alla porta = masculine singular
• la borsa è vicina alla porta = feminine singular

In this sentence, the umbrella is what is near the door, so vicino agrees with ombrello.

Alla is a contraction of:

a + la

This kind of contraction is very common in Italian:

• a + il = al
• a + lo = allo
• a + la = alla
• a + i = ai
• a + gli = agli
• a + le = alle

So alla porta literally comes from to the door, but in English we often translate it more naturally as near the door in this sentence.

Yes, it sounds polite and formal enough because of Signora and the use of formal suo.

If you were speaking informally to someone you know well, you would usually say:

Il tuo ombrello è vicino alla porta.

You could also leave out Signora entirely if you are not directly addressing the person.