L’inquilina del nuovo appartamento saluta la portinaia con gentilezza.

Because inquilina starts with a vowel, and in Italian la is normally shortened to l’ before a vowel.

• la inquilina → l’inquilina
• This is called elision

The same thing happens with other articles too, for example:

• l’amica
• l’isola
• l’ora

In writing, the apostrophe is required here.

Del is a combination of:

• di = of
• il = the

So:

• di + il = del

Here, del nuovo appartamento means of the new apartment.

This kind of contraction is very common in Italian:

• di + il = del
• di + lo = dello
• di + la = della
• di + i = dei
• di + gli = degli
• di + le = delle

Because nuovo has to agree with appartamento, not with inquilina.

• appartamento is masculine singular
• so the adjective must also be masculine singular: nuovo

Even though inquilina is feminine, that does not affect nuovo, because nuovo describes appartamento.

Compare:

• il nuovo appartamento
• la nuova casa

Saluta is the third person singular, present indicative of salutare.

So it can mean:

• he/she greets
• he/she says hello to

In this sentence, the subject is l’inquilina, so saluta means she greets.

A quick pattern:

• io saluto = I greet
• tu saluti = you greet
• lui/lei saluta = he/she greets
• noi salutiamo = we greet
• voi salutate = you all greet
• loro salutano = they greet

Because salutare takes a direct object in Italian.

So you say:

• salutare qualcuno = to greet someone

not:

• salutare a qualcuno

That is very important for English speakers, because English often uses say hello to someone, but Italian commonly uses salutare qualcuno directly.

So:

• saluta la portinaia = she greets the concierge/doorkeeper

Italian uses definite articles very often, often more than English does.

Here, the articles show that we are talking about specific people:

• l’inquilina = the tenant
• la portinaia = the concierge/doorkeeper

In English, article usage can sometimes be looser depending on context, but in Italian the article is usually required with specific nouns like these.

Portinaia is the feminine form of portinaio.

Traditionally, a portinaio / portinaia is a person who works in or looks after an apartment building, often near the entrance. Depending on context, it can be translated as:

• concierge
• doorkeeper
• building caretaker

The best English translation depends on the situation and on the variety of English being used.

They are feminine because they refer to female people.

• inquilina = female tenant
• portinaia = female concierge/doorkeeper

The corresponding masculine forms are:

• inquilino
• portinaio

This is a common pattern in Italian:

• -o often masculine
• -a often feminine

Though not every noun follows that pattern, it is very common.

Con gentilezza literally means with kindness / with politeness, and in natural English it often corresponds to kindly or politely.

Italian often uses con + noun to express manner:

• con calma = calmly
• con attenzione = carefully
• con pazienza = patiently
• con gentilezza = kindly / politely

There is no article because abstract nouns in expressions like this often appear without one.

You could also express a similar idea with an adverb:

• saluta gentilmente la portinaia

But con gentilezza is perfectly natural.

In Italian, many common descriptive adjectives can come before the noun, and nuovo often does.

So:

• il nuovo appartamento = the new apartment

This is a very normal word order.

With some adjectives, changing the position can slightly change the nuance, but for a learner the main point is:

• nuovo appartamento is standard and natural

Yes, Italian word order is somewhat flexible, but the original sentence is the most neutral.

Neutral order:

• L’inquilina del nuovo appartamento saluta la portinaia con gentilezza.

You could move parts around for emphasis, for example:

• Con gentilezza, l’inquilina del nuovo appartamento saluta la portinaia.
• La portinaia la saluta con gentilezza l’inquilina del nuovo appartamento.
  This is much less neutral and would need a specific context.

For learners, it is best to treat the original sentence as the standard pattern:

• subject + verb + object + extra information

Not necessarily. Here it identifies which tenant we mean.

So l’inquilina del nuovo appartamento means:

• the tenant of the new apartment
• in more natural English, often the tenant of the new apartment or the tenant in the new apartment, depending on context

It is a relationship phrase, not necessarily ownership.

Yes. The basic sentence would still be complete:

• L’inquilina del nuovo appartamento saluta la portinaia.

That means The tenant of the new apartment greets the concierge/doorkeeper.

Adding con gentilezza simply tells us how she does it. It adds manner, not essential grammar.