В кафе мы заказали по чашке чая.

Because кафе is an indeclinable noun in Russian. That means its form does not change across cases.

Here, в means in / at, and with location it normally takes the prepositional case. Many nouns would change form:

• в доме = in the house
• в школе = in the school

But кафе stays кафе in all cases:

• кафе
• в кафе
• из кафе

So grammatically it is still behaving as expected after в, but the noun itself just does not change.

Yes, Russian often drops subject pronouns when they are clear from context. But here мы is perfectly natural.

There are two useful reasons:

1. Clarity
   In the past tense, Russian verbs show gender and number, but not person very clearly in the same way as present tense forms do.
   заказали means ordered in the plural, but by itself it could mean:

   • we ordered
   • they ordered

   So мы makes the subject explicit: we.

2. Focus or contrast
   Including мы can also slightly emphasize who did the action:

   • В кафе мы заказали... = At the café, we ordered...

So the pronoun is not required in every context, but it is very normal here.

заказали is the past plural form of заказать, which is a perfective verb.

That matters because the sentence describes a completed action:

• We went to the café.
• We placed the order.
• The action is finished.

So заказали means something like ordered / placed an order for.

Compare:

• заказали = ordered, completed the act
• заказывали = were ordering / used to order / ordered (with more focus on process or repeated action)

In this sentence, the perfective form заказали is the natural choice because it refers to one completed event.

Here по has a distributive meaning: one each.

So:

• по чашке чая = a cup of tea each

This is a very common Russian pattern:

• по яблоку = one apple each
• по билету = one ticket each
• по книге = one book each

So Мы заказали по чашке чая does not just mean We ordered a cup of tea. It means each person in the group ordered one cup.

Because after по in this distributive meaning, Russian usually uses the dative singular.

The noun is:

• чашка = cup

Its dative singular form is:

• чашке

So:

• по чашке = one cup each

This is a pattern worth remembering:

• по чашке
• по ложке
• по книге
• по яблоку

So чашке is there because of the grammar of по.

Because чашка чая means a cup of tea, and after a container or measure word, Russian usually puts the substance in the genitive case.

So:

• чашка = cup
• чай = tea
• чашка чая = a cup of tea

This is very common in Russian:

• стакан воды = a glass of water
• чашка кофе = a cup of coffee
• бутылка молока = a bottle of milk

So чая is the genitive singular of чай, used after чашка.

Yes, it helps to read it as one chunk:

• по
  • чашке
    • чая

Structure:

• по = each / apiece
• чашке = cup, in the dative singular
• чая = tea, in the genitive singular

So literally it is something like:

• apiece one cup of tea

A good way to understand it is:

• по чашке = one cup each
• чая = of tea

Together: one cup of tea each.

Russian word order is flexible, and this order puts the setting first:

• В кафе = at the café / in the café

So the sentence begins by establishing the place, and then tells what happened there:

• В кафе мы заказали по чашке чая.
• At the café, we ordered a cup of tea each.

Other word orders are also possible, with different emphasis:

• Мы заказали по чашке чая в кафе.
  More neutral, with the place added later.

• По чашке чая мы заказали в кафе.
  Stronger focus on what was ordered.

So the original order is natural and very common for setting the scene first.

No. Because of по, it specifically means one cup each.

Without по, the meaning would change:

• Мы заказали чашку чая.
  = We ordered a cup of tea.
  This could mean one cup total.

But:

• Мы заказали по чашке чая.
  = We ordered a cup of tea each.

So по is the key word that gives the distributive meaning.

Yes. In English, the best translation depends on context.

Russian в кафе literally means in the café, but in natural English it is often translated as:

• at the café
• in the café

Both can work. English chooses between in and at based on style and context, but Russian simply uses в here.

So in many situations:

• В кафе мы заказали по чашке чая. can be translated naturally as:
• At the café, we ordered a cup of tea each.

Yes. That would be more explicit:

• по чашке чая = a cup of tea each
• по одной чашке чая = one cup of tea each

Adding одной emphasizes the number one more clearly. Often it is unnecessary, because по чашке already naturally means one cup each.

So the original sentence is shorter and very natural.