В кафе за чай и пирожное взяли больше, чем мы ожидали.

Russian often uses the 3rd person plural with no stated subject to mean people / they / someone when the exact doer is not important.

So взяли literally means they took, but here it refers to the café staff in a general way. In English, we often translate this more naturally as they charged.

A fuller version could be:

В кафе за чай и пирожное с нас взяли больше, чем мы ожидали.

Here с нас means from us, but Russian often leaves it out if it is obvious.

Because in Russian, взять can be used in money contexts to mean take a certain amount from someone, so in natural English that often becomes charge.

For example:

За обед взяли 1000 рублей.
= They charged 1000 rubles for lunch.

So in your sentence, взяли больше means they took more money than expected → they charged more than we expected.

Here за means for, in the sense of for an item or service you are paying for.

So:

• за чай = for the tea
• за пирожное = for the pastry / cake

This is a very common pattern in Russian:

• заплатить за кофе = to pay for coffee
• взять за ремонт = to charge for the repair

After за in this meaning, Russian uses the accusative case.

So both nouns are in the accusative:

• чай → accusative singular
• пирожное → accusative singular

They look unchanged because they are inanimate nouns:

• masculine inanimate nouns often have accusative = nominative
• neuter inanimate nouns also have accusative = nominative

So:

• чай stays чай
• пирожное stays пирожное

Because в + prepositional case is used for being in / at a place.

So:

• в кафе = in the café / at the café

Also, кафе is an indeclinable noun, so its form does not change across cases. That is why it is still кафе, not something like a changed ending.

Пирожное is a singular neuter noun meaning a small cake, pastry, or fancy dessert item.

It does not mean the same thing as:

• пирог = pie / large baked dish
• пирожок = small stuffed bun or turnover
• торт = cake

So чай и пирожное is a very typical café combination: tea and a pastry/cake.

Russian often leaves out a noun if it is obvious from context.

Here больше means something like:

• more money
• a higher amount

So взяли больше really means they charged more money.

Russian does this a lot when the missing word is easy to understand.

Because чем is the normal word used after a comparative such as:

• больше = more
• меньше = less
• лучше = better

So:

• больше, чем... = more than...
• лучше, чем... = better than...

In your sentence:

больше, чем мы ожидали
= more than we expected

You cannot use что here, because this is a comparison, and Russian uses чем for that.

Because the subject is мы = we.

In the past tense, Russian verbs agree with the subject in number, and in the singular also in gender.

So:

• я ожидал / ожидала = I expected
• мы ожидали = we expected

That is why the sentence has ожидали.

No, Russian word order is fairly flexible.

This order is natural because it presents the information in a clear sequence:

1. В кафе — the setting
2. за чай и пирожное — what the charge was for
3. взяли больше — the main point
4. чем мы ожидали — the comparison

You could rearrange parts of the sentence, but the emphasis would shift. For example:

За чай и пирожное в кафе взяли больше, чем мы ожидали.

This is also correct, but it puts slightly more focus on what was being paid for.

Yes. A more explicit version would be:

В кафе за чай и пирожное с нас взяли больше, чем мы ожидали.

с нас literally means from us.

Russian often omits it when the meaning is already clear, especially if the sentence is just reporting the price charged. So the shorter version sounds natural too.