Ne bi trebalo usisavati blagovaonicu dok beba spava.

It is a common Croatian way to express should not.

So:

• trebalo bi = should
• ne bi trebalo = should not

Literally, it is closer to something like it would not be advisable / it would not be appropriate, but in normal English shouldn’t is the best match.

Bi is the conditional auxiliary. Croatian often uses the conditional to make advice or obligation sound softer and less direct.

So:

• Ne treba usisavati... = more direct; can mean you shouldn’t vacuum... or there’s no need to vacuum...
• Ne bi trebalo usisavati... = softer, more like you shouldn’t be vacuuming...

This is a very common pattern in Croatian.

Because this is an impersonal construction.

There is no stated subject like ja, ti, or mi, so Croatian uses the neuter singular form trebalo.

Compare:

• Trebalo bi otići. = One should go.
• Ne bi trebalo pušiti. = One shouldn’t smoke.

English often uses you, one, or just people in these situations, but Croatian often leaves the subject unspecified.

After (ne) bi trebalo, Croatian normally uses an infinitive to name the action.

So the pattern is:

• (ne) bi trebalo + infinitive

Examples:

• Trebalo bi učiti. = One should study.
• Ne bi trebalo kasniti. = One shouldn’t be late.
• Ne bi trebalo usisavati... = One shouldn’t vacuum...

This is about aspect.

• usisavati = imperfective
• usisati = perfective

Here, usisavati fits better because the sentence is talking about the activity in progress or as a general action: don’t be vacuuming while the baby is asleep.

With dok beba spava, the imperfective sounds natural because the two actions overlap in time:

• vacuuming
• the baby sleeping

Using usisati would sound more like a single completed act of vacuuming the room, which is less natural in this kind of general warning.

Because it is the accusative singular form of blagovaonica.

Blagovaonica is a feminine noun ending in -a, and feminine nouns of this type usually change -a to -u in the accusative singular.

So:

• nominative: blagovaonica
• accusative: blagovaonicu

It is accusative here because it is the direct object of usisavati.

Yes, and that is normal.

In Croatian, verbs like usisavati can take the room itself as the direct object:

• usisavati sobu
• usisavati dnevni boravak
• usisavati blagovaonicu

This means to vacuum the floor/carpeting in that room.

If you said usisavati u blagovaonici, that would emphasize the location: to vacuum in the dining room.
The original sentence treats the dining room as the thing being cleaned.

It is not expressed, because the sentence is impersonal.

Croatian often avoids naming the subject when the meaning is general. English usually has to choose something:

• you shouldn’t vacuum...
• one shouldn’t vacuum...
• people shouldn’t vacuum...

Croatian can simply say:

• Ne bi trebalo usisavati...

That sounds natural and general.

Because dok means while, and Croatian normally uses the present tense for an action happening at the same time as another action.

So:

• dok beba spava = while the baby sleeps / is sleeping

Croatian does not have a separate continuous form like English is sleeping, so the plain present spava covers both ideas.

Because Croatian has no articles.

So Croatian does not have separate words for a/an/the.
That means:

• beba can mean a baby or the baby
• blagovaonicu can mean a dining room or the dining room

The context tells you which meaning is intended.

Yes, you could.

But there is a nuance:

• Ne bi trebalo... = softer, more like advice or recommendation
• Ne treba... = more direct; sometimes there’s no need to..., sometimes you shouldn’t...

So ne bi trebalo is often the better choice when you want to sound polite or less blunt.

Yes. Croatian word order is fairly flexible.

For example:

• Ne bi trebalo usisavati blagovaonicu dok beba spava.
• Dok beba spava, ne bi trebalo usisavati blagovaonicu.

Both are natural.

The difference is mostly about emphasis:

• starting with Ne bi trebalo... emphasizes the advice
• starting with Dok beba spava... emphasizes the time condition

No, but it is a standard and very good word to learn.

You may also hear trpezarija in some regions or styles.
Still, blagovaonica is a safe standard Croatian choice.