È da stamattina che il cassiere aspetta il segretario per firmare il modulo.

This is a very common Italian pattern for an action that started in the past and is still continuing now:

È da + time expression + che + present tense

So È da stamattina che il cassiere aspetta... means something like:

The cashier has been waiting since this morning...

Literally, it is closer to It’s since this morning that the cashier is waiting, but that sounds unnatural in English. Italian uses this structure very naturally.

Because in Italian, when you talk about an action that began in the past and continues into the present, you often use the present tense with da.

So:

aspetta da stamattina
means
has been waiting since this morning

English usually uses the present perfect or present perfect continuous, but Italian normally uses the present here.

Compare:

Aspetto da un’ora. = I have been waiting for an hour.

Not I wait for an hour in English, but that is how Italian structures it.

It can correspond to either one, depending on what comes after it.

• da stamattina = since this morning → a starting point
• da due ore = for two hours → a duration

In both cases, the idea is that the action is still ongoing.

So here, da stamattina means since this morning.

Here che introduces the clause containing the action: il cassiere aspetta il segretario.

It is part of the fixed pattern È da... che.... You should think of it as a whole structure, not as a separate word you translate one by one.

You can also say the same thing without this structure:

Il cassiere aspetta il segretario da stamattina.

That version is a bit more straightforward.
The version with È da stamattina che... puts extra focus on the length of time.

Yes. Sta aspettando is also possible.

Compare:

• È da stamattina che il cassiere aspetta il segretario.
• È da stamattina che il cassiere sta aspettando il segretario.

Both are grammatical. The version with sta aspettando highlights the ongoing process a bit more, like has been sitting there waiting. But the simple present aspetta is already very natural and common in this kind of sentence.

Per + infinitive is the normal way to express purpose in Italian:

per firmare = to sign / in order to sign

So aspetta il segretario per firmare il modulo means that the waiting is connected to the goal of signing the form.

This is one of the most common uses of per:

• Studio per imparare. = I study to learn.
• È uscito per comprare il pane. = He went out to buy bread.

Grammatically, per firmare il modulo usually refers to the same subject as the main verb, so the most natural grammatical reading is that the cashier is the one who will sign.

That is because the main subject is il cassiere, and the infinitive firmare has no separate stated subject.

If you want to make it clearly mean that the secretary is supposed to sign, Italian would normally rephrase it, for example:

• ... aspetta il segretario perché firmi il modulo
• ... aspetta che il segretario firmi il modulo
• ... per far firmare il modulo al segretario

So yes, this part can feel ambiguous to an English speaker, but the default grammatical link is usually to il cassiere.

Italian uses articles more often than English does.

Here, the articles suggest specific people and a specific document known in the situation:

• il cassiere = the cashier
• il segretario = the secretary
• il modulo = the form

With professions and ordinary count nouns, Italian normally needs an article unless there is some special reason to omit it.

Yes, stamattina is very commonly written as one word, and it means this morning.

You can also say questa mattina. The meaning is basically the same in most contexts.

So these are both possible:

• È da stamattina che aspetta.
• È da questa mattina che aspetta.

Stamattina is especially common in everyday spoken Italian.

Yes. A simpler version is:

Il cassiere aspetta il segretario da stamattina per firmare il modulo.

This means essentially the same thing. The original sentence:

È da stamattina che il cassiere aspetta il segretario...

sounds a bit more focused on the duration, as if stressing since this morning.

So both are correct, but the original has a little more emphasis.