Quello di cui ho bisogno adesso è un po’ di tranquillità.

In this sentence, quello does not mean just that one in the ordinary demonstrative sense. It is being used as a pronoun meaning the thing that or what.

So:

Quello di cui ho bisogno
= The thing that I need / What I need

This is a very common Italian structure. English often uses what, while Italian often uses quello che or quello di cui, depending on the verb and whether a preposition is required.

Because the expression avere bisogno requires the preposition di:

avere bisogno di qualcosa = to need something
literally, to have need of something

When a relative pronoun comes after a preposition in Italian, cui is normally used:

• la cosa di cui ho bisogno = the thing I need
• literally: the thing of which I have need

So:

quello di cui ho bisogno
is correct because bisogno needs di.

You cannot normally say quello che ho bisogno in standard Italian, because che cannot replace di cui here.

Italian often expresses to need with the idiomatic phrase avere bisogno di.

So:

• Ho bisogno di riposo = I need rest
• Abbiamo bisogno di aiuto = We need help

There is also the verb necessitare, but it is much less common in everyday speech and often sounds more formal or bureaucratic.

So ho bisogno di is the most natural choice in ordinary Italian.

It is masculine singular because it refers to an abstract idea: the thing that is needed. In Italian, when a pronoun refers to something unspecified or abstract, masculine singular is often used by default.

So quello here does not point to a masculine noun already mentioned. It just means something like that thing / what in a general, neutral sense.

Adesso means now or right now. It tells you when the need exists.

So:

di cui ho bisogno adesso
= that I need now

Its position is flexible. You could also say:

• Quello di cui adesso ho bisogno...
• Adesso, quello di cui ho bisogno...

But the original placement sounds natural and smooth.

In this sentence, adesso modifies ho bisogno: it is the needing that is happening now.

Un po’ di means a little bit of or some.

Examples:

• un po’ di tempo = a little time
• un po’ di acqua = a little water
• un po’ di tranquillità = a bit of peace and quiet

It is used before nouns, especially uncountable or abstract nouns.

Also note the spelling: po’ has an apostrophe because it is a shortened form of poco. So the standard spelling is un po’, not un pò.

Because after un po’ di, Italian normally uses just di + noun, without an article:

• un po’ di pane
• un po’ di pazienza
• un po’ di tranquillità

This works much like English a bit of peace and quiet or some tranquility.

Adding an article here would usually sound unnatural.

Tranquillità means tranquility, calm, peace, or peace and quiet, depending on context.

In this sentence, it probably means something like:

• some peace and quiet
• a bit of calm
• some tranquility

It is an abstract noun, so it fits very naturally after un po’ di.

The sentence has this structure:

[subject] + è + [complement]

Here the subject is the whole phrase:

Quello di cui ho bisogno adesso
= What I need right now

Then comes the verb:

è = is

Then the complement:

un po’ di tranquillità
= a bit of tranquility / peace and quiet

So the sentence is built like:

What I need right now is a bit of peace and quiet.

Yes. A simpler and more direct version would be:

Ho bisogno di un po’ di tranquillità adesso.

That means essentially the same thing: I need a bit of peace and quiet right now.

The original sentence,

Quello di cui ho bisogno adesso è un po’ di tranquillità,

is a little more structured and emphatic. It puts extra focus on what it is that the speaker needs.

So:

• Ho bisogno di un po’ di tranquillità adesso = more direct
• Quello di cui ho bisogno adesso è un po’ di tranquillità = more emphatic, more like What I need right now is...

Yes. Ciò di cui ho bisogno is also correct and means almost the same thing.

However:

• quello di cui ho bisogno is more common in everyday Italian
• ciò di cui ho bisogno sounds a bit more formal or literary

So in normal conversation, quello di cui ho bisogno is usually the more natural choice.