Alla cassa c’è una fila lunga, quindi Anna controlla il telefono mentre aspetta.

Alla cassa means at the checkout / at the cash register.

It is made of:

• a = to / at
• la = the

These combine into:

• a + la = alla

In Italian, alla cassa is the normal expression for being at the supermarket checkout or cashier area. English often says at the checkout, and Italian uses alla cassa in the same kind of way.

Here, cassa means cash register, checkout, or till, depending on context.

So:

• alla cassa = at the checkout
• in cassa can sometimes be used in other contexts, but alla cassa is the standard phrase when talking about where customers line up to pay.

C’è means there is.

It is formed from:

• ci = there
• è = is

So:

• c’è una fila lunga = there is a long line

If you said just è una fila lunga, that would mean something more like it is a long line, which is not what the sentence is trying to say.

This is a very common Italian structure:

• C’è un problema. = There is a problem.
• C’è molta gente. = There are a lot of people.
  (Italian often still uses singular c’è with some expressions in speech, though standard grammar also has ci sono for plural.)

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

• una fila lunga is the most neutral, everyday way to say a long line
• una lunga fila is also correct, but it can sound a little more descriptive, literary, or emphatic

In simple everyday speech, Italians often put many descriptive adjectives after the noun:

• una casa grande
• un libro interessante
• una fila lunga

So in this sentence, una fila lunga sounds very natural.

Quindi means so, therefore, or as a result.

Here it connects the two ideas:

• there is a long line
• as a result, Anna checks her phone while she waits

So:

• Alla cassa c’è una fila lunga, quindi Anna controlla il telefono...

It often appears in the middle of a sentence like this, but it can also begin a sentence:

• Alla cassa c’è una fila lunga. Quindi Anna controlla il telefono.

In everyday speech, allora can sometimes be used in a similar way, but quindi is a clear logical connector.

Yes. Controllare il telefono commonly means to check one’s phone.

Italian often uses the definite article where English uses a possessive adjective:

• controlla il telefono = she checks her phone
• not necessarily the phone in a literal English sense

This happens a lot when the owner is obvious from context:

• Mi lavo le mani = I wash my hands
• Ha chiuso gli occhi = He/She closed his/her eyes
• Anna controlla il telefono = Anna checks her phone

So even though Italian says the phone, English usually translates it as her phone here.

It could say il suo telefono, but that is often unnecessary.

Italian prefers il telefono when it is already clear whose phone it is. Since the subject is Anna, we naturally understand that she is checking her own phone.

Using il suo telefono would add emphasis or contrast, for example:

• Anna controlla il suo telefono, non quello di Marco. = Anna checks her phone, not Marco’s.

So in the original sentence, il telefono is the most natural choice.

Italian often omits subject pronouns because the verb ending already tells you who the subject is.

Here:

• controlla = he/she checks
• aspetta = he/she waits

Because Anna is already named, there is no need to add lei.

So:

• Anna controlla il telefono mentre aspetta is more natural than:
• Anna controlla il telefono mentre lei aspetta

Italian usually includes pronouns like io, tu, lui, lei only for emphasis, contrast, or clarity.

The subject is understood to be Anna.

So:

• Anna controlla il telefono mentre aspetta means
• Anna checks her phone while she waits

Italian often leaves the subject unstated in subordinate clauses when it is the same as the main subject.

If the subject were different, Italian would usually make that clearer:

• Anna controlla il telefono mentre Marco aspetta. = Anna checks her phone while Marco waits.

Mentre means while, so it emphasizes that two actions happen at the same time.

• Anna controlla il telefono mentre aspetta. = Anna checks her phone while she waits.

Quando means when, which is more general and does not always stress simultaneity in the same way.

• Anna controlla il telefono quando aspetta. would mean something like Anna checks her phone when she is waiting, more as a general habit or circumstance.

So mentre is the best choice here because the sentence is describing two actions happening at the same time.

Italian uses the simple present very often for actions happening right now, much more than English does.

So:

• Anna controlla il telefono mentre aspetta can mean
• Anna is checking her phone while she waits or more naturally in English,
• Anna checks her phone while she waits

English often prefers the present continuous (is checking), but Italian normally just uses the present:

• mangio = I eat / I am eating
• legge = he/she reads / is reading
• aspetta = he/she waits / is waiting

Yes. Fila has a few related meanings, including:

• line / queue of people
• row of seats, desks, etc.

In this sentence, because of alla cassa, it clearly means a line / queue.

Examples:

• C’è una fila lunga alla cassa. = There’s a long line at the checkout.
• Siamo in prima fila. = We are in the first row.

So the context tells you which meaning is intended.

Yes, it sounds very natural.

Everything in it is standard and common:

• alla cassa
• c’è una fila lunga
• quindi
• controlla il telefono
• mentre aspetta

A native speaker would easily say or understand this sentence in an everyday situation.