После урока мы сделали обложку для проекта и убрали клей в ящик.

Because после requires the genitive case.

• урок = nominative
• урока = genitive singular

So:

• после урока = after the lesson / after class

This is a very common pattern in Russian:

• после работы = after work
• после школы = after school
• после фильма = after the movie

In this sentence, урок most naturally means lesson or class period.

So после урока can mean:

• after the lesson
• after class

In school contexts, Russian урок often refers to one class session, not the general idea of education.

Сделали is the perfective past tense of сделать, while делали is the imperfective past tense of делать.

Here, сделали is used because the sentence presents the action as completed:

• мы сделали обложку = we made / finished the cover

If you said мы делали обложку, it would mean more like:

• we were making the cover
• we worked on the cover

So the perfective form fits because the sentence describes completed results.

Because обложку is in the accusative case, which is used for the direct object of the verb.

• обложка = nominative
• обложку = accusative singular

Here, the thing being made is the cover:

• сделали что? → обложку

So:

• мы сделали обложку = we made a cover

Обложка means cover, usually the outer cover of something such as:

• a book
• a notebook
• a report
• a school project

In обложка для проекта, it means the cover page or outer cover for the project.

Because для means for, and it requires the genitive case.

• проект = nominative
• проекта = genitive singular

So:

• для проекта = for the project

This is another very common pattern:

• для друга = for a friend
• для школы = for school
• для учителя = for the teacher

Again, this is the perfective vs. imperfective distinction.

• убрали = perfective, completed action
• убирали = imperfective, process or repeated action

In this sentence:

• убрали клей в ящик = put the glue away into the drawer

The speaker is describing a finished action, so убрали is the natural choice.

Also, убрать often means not just clean up, but put away / remove to its proper place.

Because клей is the direct object, and for an inanimate masculine noun, the accusative singular is the same as the nominative singular.

• nominative: клей
• accusative: клей

So:

• убрали что? → клей

That is why it stays клей.

By contrast, some other nouns do change in the accusative:

• книга → книгу
• тетрадь → тетрадь (same spelling, different case function)

Because в can take either the accusative or the prepositional, depending on meaning.

Here the meaning is motion into the drawer, so Russian uses the accusative:

• в ящик = into the drawer

Compare:

• клей в ящике = the glue is in the drawer
  
  • location, so prepositional
• убрали клей в ящик = put the glue into the drawer
  
  • movement/direction, so accusative

This is a very important Russian pattern:

• в школу = to school
• в школе = at school
• на стол = onto the table
• на столе = on the table

Literally, it may feel a little unusual in English, but in natural Russian it means:

• put the glue away in/into the drawer

Russian убрать often means:

• to remove
• to put away
• to tidy away

So убрать что-то в ящик means to put something away into a drawer, cupboard, box, etc.

Yes, Russian often can omit the subject pronoun because the verb ending already shows the person and number.

• сделали already means we/they did
• in context, it could be understood as we did

But мы is often included when the speaker wants to:

• make the subject explicit
• sound clearer
• emphasize we

So both are possible:

• После урока сделали обложку... = After class, we made a cover...
• После урока мы сделали обложку... = same meaning, with explicit we

Because и is simply joining two verbs with the same subject:

• мы сделали
• (мы) убрали

This is one sentence with a shared subject, so no comma is needed.

A comma would normally appear only if there were a more complex structure, such as separate clauses that required it for another reason.

Yes, Russian word order is fairly flexible.

All of these are possible, depending on emphasis:

• После урока мы сделали обложку...
• Мы после урока сделали обложку...
• Обложку для проекта мы сделали после урока...

The original order is natural because it starts with the time expression:

• После урока = after class

Then it gives the main actions.

Russian word order often changes to highlight:

• time
• topic
• contrast
• new information

Here are the main dictionary forms:

• после = after
• урок = lesson, class
• мы = we
• сделать = to make, to do, to complete
• обложка = cover
• для = for
• проект = project
• убрать = to put away, remove, tidy away
• клей = glue
• в = in, into
• ящик = drawer, box

This is useful because many forms in the sentence are not in the dictionary form:

• урока ← урок
• обложку ← обложка
• проекта ← проект
• сделали ← сделать
• убрали ← убрать

Here is the full case breakdown:

• После урока

  • урока = genitive, because после requires genitive

• мы

  • nominative subject

• сделали обложку

  • обложку = accusative, direct object

• для проекта

  • проекта = genitive, because для requires genitive

• убрали клей

  • клей = accusative, direct object
  • it looks like nominative because it is inanimate masculine singular

• в ящик

  • ящик = accusative, because it shows movement into something

So the sentence gives a nice example of how Russian cases depend on both verbs and prepositions.