V restauraci jsme si objednali polévku a moje dcera chce ještě malý dezert.

Because v meaning in takes the locative case when it shows location.

• Dictionary form: restaurace
• After v for location: v restauraci = in the restaurant

So the noun changes form because of the preposition.
Compare:

• v restauraci = in the restaurant
• do restaurace = to the restaurant

Czech often leaves out subject pronouns because the verb form already tells you who is doing the action.

• jsme = we are / we have as an auxiliary here
• So jsme objednali already tells you the subject is we

You could add my for emphasis or contrast:

• My jsme si objednali polévku, ale oni ne.
  = We ordered soup, but they didn’t.

In a neutral sentence, leaving my out is normal.

This is the past tense of objednat si = to order for oneself / to order.

It breaks down like this:

• jsme = auxiliary verb
• si = reflexive word, here meaning something like for ourselves
• objednali = past participle

So jsme si objednali polévku means we ordered soup.

The si is very common with verbs like this when the action is done for your own benefit. In a restaurant, objednat si is very natural.

In Czech past tense, the participle agrees with the subject in number and often also gender.

• objednali is used for:
  • a group of men, or
  • a mixed group that includes at least one male

If the group were only women, it would be:

• objednaly

So this sentence suggests that the we group is either mixed or includes a male speaker.

Because polévku is the accusative singular form, and it is the direct object of ordered.

• Dictionary form: polévka = soup
• Direct object form: polévku

This is a very common pattern for feminine nouns ending in -a:

• káva → kávu
• voda → vodu
• polévka → polévku

Because the two actions are being viewed at different times.

• jsme si objednali polévku = we already ordered the soup
• moje dcera chce ještě malý dezert = my daughter now wants another small dessert

So the sentence mixes past and present naturally:

1. one thing has already happened
2. another desire is current

If you were telling the whole thing entirely as a past story, you might say chtěla instead of chce.

Both are correct and both mean my daughter.

• moje dcera
• má dcera

In everyday Czech, moje is very common and sounds natural in speech.
má is also correct, but can sound a bit more formal, literary, or sometimes more emphatic depending on context.

So for a learner, the important thing is: both are normal, but moje dcera is very common in conversation.

Ještě can mean different things depending on context, including:

• still
• yet
• more
• another
• also

In this sentence, it most naturally means something like:

• another
• one more
• an extra

So moje dcera chce ještě malý dezert means that the daughter wants an additional small dessert.

It is in the accusative, but dezert is a masculine inanimate noun, and in the singular its accusative looks the same as the nominative.

So:

• nominative: malý dezert
• accusative: malý dezert

That is why there is no visible change here.

Compare that with a masculine animate noun, where you would see a change:

• nominative: malý pes
• accusative: malého psa

Yes. Czech word order is more flexible than English word order.

The given sentence is a natural neutral version:

• V restauraci jsme si objednali polévku...

Starting with V restauraci sets the scene first: In the restaurant...

Other word orders are possible, for example:

• Objednali jsme si v restauraci polévku...

But the emphasis changes slightly. Czech often moves things around to show what is already known, what is new, or what is being emphasized.

One important detail: short words like jsme and si usually stay near the beginning of the clause, in the so-called second position, so learners will often see patterns like:

• V restauraci jsme si objednali...
• Dnes jsme si objednali...
• Pak jsme si objednali...

So yes, the order can change, but not completely freely.