Ŝi deponis monon sen ke dungito demandis ion.

Because mono is the direct object of deponis.

In Esperanto, direct objects usually take -n:

• Ŝi deponis monon. = She deposited money.
• Ŝi vidis dungiton. = She saw an employee.

So monon shows what was deposited.

For the same reason: ion is the direct object of demandi.

• demandi ion = to ask something
• demandi demandon = to ask a question

Here, the employee did not ask anything, and Esperanto uses ion as the object.

A useful point for English speakers: Esperanto often uses io/ion where English would use anything in a negative or negative-like context:

• Mi ne vidis ion. can mean I didn’t see anything
• sen ke dungito demandu ion = without an employee asking anything

Esperanto has no indefinite article. There is la for the, but there is no separate word for a/an.

So:

• dungito = an employee / employee
• la dungito = the employee

If you want to emphasize some employee, you could say iu dungito, but plain dungito is often enough.

sen ke means without ... when what follows is a full clause with its own verb.

Here, the part after it has its own subject and verb:

• dungito = subject
• demandu/demandis = verb

So Esperanto uses a clause:

• sen ke dungito demandu ion

The word ke introduces that clause, similar to how that can introduce a clause in English, though English usually says this differently.

Yes, but it would mean something different.

• Ŝi deponis monon sen demandi ion.
  = She deposited money without asking anything.

In that version, the understood subject of demandi is the same as the main subject, ŝi.

But in your sentence, the one who would ask is dungito, not ŝi. Because the subject changes, Esperanto normally uses sen ke + a finite verb:

• Ŝi deponis monon, sen ke dungito demandu ion.

Many speakers would prefer demandu here:

• Ŝi deponis monon, sen ke dungito demandu ion.

This is because after sen ke, Esperanto often uses the -u form when the action in the subordinate clause is something that did not happen.

So demandu here does not mean a command. It is the usual grammatical choice for a clause like:

• without an employee asking anything

The version with demandis is understandable, but many learners will be taught that demandu is the more standard or more natural form in this structure.

No. That is a very common beginner misunderstanding.

The -u ending is often called the volitive form. It is used for:

• commands: Venu! = Come!
• wishes: Li estu feliĉa. = May he be happy.
• purpose and similar subordinate clauses: por ke, sen ke, and others

So in:

• sen ke dungito demandu ion

the -u does not mean Let the employee ask something. It simply fits the grammar after sen ke, where the asking is not presented as a real completed event.

Usually, yes. Many writers would punctuate it like this:

• Ŝi deponis monon, sen ke dungito demandu ion.

A comma before a subordinate clause is very common in Esperanto and often clearer than English punctuation.

So the sentence without a comma is not hard to understand, but the version with a comma will usually look more natural.

A very natural version would be:

• Ŝi deponis monon, sen ke dungito demandu ion.

If you want to make an employee sound a bit more explicit, you could also say:

• Ŝi deponis monon, sen ke iu dungito demandu ion.

Both are understandable, but the first one is already good Esperanto.