Между лекциями мы заходим в буфет и берём по чашке чая, но сегодня в буфете не было кефира.

Because между normally takes the instrumental case when it means between.

• лекции = lectures
• instrumental plural = лекциями

So между лекциями literally means between lectures. This is a very common time expression in Russian.

This is the usual Russian contrast between motion toward a place and location in a place:

• в буфет = to the cafeteria/snack bar → movement, so Russian uses the accusative
• в буфете = in the cafeteria/snack bar → location, so Russian uses the prepositional

With masculine inanimate nouns like буфет, the accusative singular looks the same as the nominative, so you see буфет with no ending change.

Because the first part describes a usual, repeated action: what we normally do between lectures.

In Russian, the present tense of an imperfective verb is often used for habits and routines:

• заходим = we go in / we stop by
• берём = we take

So this is like English We usually go to the snack bar and get...

Because the sentence is about a habit, not one completed event.

• заходить and брать are imperfective
• imperfective present can describe repeated or regular actions
• the perfective forms зайти and взять do not normally have a true present meaning; their present forms usually refer to the future

So:

• мы заходим, берём = we do this regularly
• мы зайдём, возьмём = we will go in, we will take

Заходить often means to go in, to drop in, or to stop by for a short time.

So заходим в буфет suggests not just movement, but the idea of popping into the buffet/cafeteria during a break. It sounds more natural than a plain motion verb if the point is a brief visit.

This is a very common Russian pattern:

• по + dative can mean one each or apiece
• чашке is the dative singular of чашка

So берём по чашке чая means we each take a cup of tea.

This по + dative pattern is often used with food, drink, and counted items:

• по билету = one ticket each
• по яблоку = one apple each
• по чашке чая = a cup of tea each

Because after a container or measure word, Russian often puts the substance in the genitive:

• чашка чая = a cup of tea
• стакан воды = a glass of water
• бутылка молока = a bottle of milk

So in по чашке чая:

• чашке is dative because of по
• чая is genitive because it depends on чашка

Because Russian commonly uses the genitive in negative existential sentences—sentences meaning there was no... / there wasn't any...

So:

• был кефир = there was kefir
• не было кефира = there was no kefir / there wasn’t any kefir

This is especially normal after не было, which is a standard way to express absence in the past.

Russian usually expresses absence/existence with быть in an impersonal-style construction:

• было молоко = there was milk
• не было молока = there was no milk

So в буфете не было кефира is the natural way to say There was no kefir in the buffet/cafeteria.

Also, было is neuter singular, which is the normal past-tense form in this kind of existential construction.

In this context, буфет usually means a snack bar, canteen counter, or small cafeteria, especially in a school, university, theater, or office building.

It does not necessarily mean an English-style buffet where food is laid out for self-service. The Russian word is related historically, but the everyday meaning is often closer to cafeteria counter or snack bar.

Russian can drop subject pronouns when the verb ending already makes the subject clear. So заходим by itself already implies we.

But including мы is still perfectly normal. It can make the sentence:

• clearer
• a bit more explicit
• slightly more contrastive or topical

So both are possible:

• Между лекциями заходим в буфет...
• Между лекциями мы заходим в буфет...

The version with мы is very natural and not unusually emphatic here.

Yes. Russian word order is fairly flexible, and changing it often changes focus rather than basic meaning.

For example, you could also hear:

• Между лекциями мы заходим в буфет и берём по чашке чая.
• Мы между лекциями заходим в буфет и берём по чашке чая.
• Но сегодня кефира в буфете не было.
• Но сегодня в буфете кефира не было.

The original sentence sounds neutral and natural. In the second clause, в буфете before не было кефира helps set the scene first: as for the buffet, there was no kefir there today.