В университете мы обычно обедаем в столовой после второй пары.

Because в can mean in or at when talking about location, and with location it usually takes the prepositional case.

• университет = university
• в университете = in/at the university

So this part means at the university or in the university setting.

Compare:

• в университете = at the university (location)
• в университет = into the university (direction, accusative)

For the same reason: after в meaning in/at a place, Russian uses the prepositional case.

• столовая = cafeteria / canteen
• prepositional singular: в столовой = in the cafeteria

This noun happens to be feminine, so its prepositional singular ends in -ой.

Обедаем is the 1st person plural form of обедать, which means to have lunch or to eat lunch.

So:

• я обедаю = I have lunch
• мы обедаем = we have lunch

In this sentence, мы обычно обедаем means we usually have lunch.

Because the sentence describes a habit or usual repeated action: we usually have lunch.

Russian often uses the imperfective for:

• habits
• repeated actions
• general facts
• ongoing processes

So обедать is the natural choice here.

A perfective verb would suggest a completed single event, which does not fit well with обычно.

Обычно means usually. It shows that the action happens regularly.

In this sentence:

• мы обычно обедаем = we usually have lunch

Russian word order is flexible, so обычно can move around for emphasis:

• Мы обычно обедаем в столовой.
• Обычно мы обедаем в столовой.

Both are normal. The version in your sentence sounds neutral and natural.

After после Russian uses the genitive case.

So:

• после = after
• вторая пара = the second class period
• genitive singular: второй пары

That is why you get:

• после второй пары = after the second class / after the second period

Literally, пара can mean pair, but in university context it often means a class period, especially a double period.

In many Russian-speaking universities, a пара is one standard teaching block, often about 90 minutes.

So:

• первая пара = first class period
• вторая пара = second class period

In this sentence, после второй пары means after the second class or after the second period, not after the second pair of something.

Actually, второй is just the form you see in the phrase because of case.

The basic nominative form is:

• вторая пара = second class period

But after после, the noun phrase goes into the genitive:

• второй пары

So вторая changes to второй because it must agree with пары in:

• gender: feminine
• number: singular
• case: genitive

Yes, very often.

Russian verb endings usually show the subject clearly, so:

• Мы обычно обедаем в столовой после второй пары.
• Обычно обедаем в столовой после второй пары.

Both can work.

Including мы can make the sentence:

• a bit clearer
• slightly more explicit
• more natural if you want to emphasize we

Not really. They give two different layers of location:

• в университете = at the university, in the general setting
• в столовой = in the cafeteria, the specific place

So the sentence means something like:

• At the university, we usually have lunch in the cafeteria after the second class period.

The first phrase sets the broader context, and the second gives the exact location.

Yes, the word order is natural.

Current sentence:

• В университете мы обычно обедаем в столовой после второй пары.

This sounds like:

• At university, we usually have lunch in the cafeteria after the second class.

Russian word order can be changed depending on emphasis. For example:

• Мы обычно обедаем в столовой после второй пары в университете.
  This is less natural if you mean the general setting at university.
• После второй пары мы обычно обедаем в столовой.
  This emphasizes the time first.
• Обычно мы обедаем в столовой после второй пары.
  Very natural too.

So the original order is a good neutral choice.

Usually no, at least not in normal modern English.

Обедать means to have lunch or sometimes to eat a midday meal. In many contexts, dine sounds too formal or refers more to an evening meal.

So the best translation here is:

• we usually have lunch
• possibly we usually eat lunch

Without обычно, the sentence becomes more like a plain statement of fact for a schedule or routine, but it loses the explicit meaning of usually.

• В университете мы обедаем в столовой после второй пары.

This can mean:

• At university, we have lunch in the cafeteria after the second class.

It may still imply routine from context, but обычно makes that routine much clearer.