Сначала учительница показала нам простой эскиз, а потом поставила мольберт рядом с окном.

Учительница is the feminine form of teacher, so it tells you the teacher is a woman.

• учитель = male teacher / teacher in a general masculine form
• учительница = female teacher

That is why the verbs are also in feminine past tense forms:

• показала
• поставила

If the teacher were a man, you would have:

• Сначала учитель показал нам простой эскиз, а потом поставил мольберт рядом с окном.

In Russian, past tense verbs agree with gender and number.

For singular subjects:

• masculine: usually no -а ending, e.g. показал
• feminine: -а, e.g. показала
• neuter: -о, e.g. показало
• plural: -и, e.g. показали

Since учительница is feminine singular, both verbs are feminine singular too:

• учительница показала
• учительница поставила

Because the verb показать / показывать often works like to show someone something.

So in Russian:

• кто? = who did it → учительница
• что? = what was shown → простой эскиз
• кому? = to whom → нам

That means нам is in the dative case.

Compare:

• мы = we
• нас = us (often genitive/accusative)
• нам = to us

So показала нам простой эскиз literally means showed to us a simple sketch.

Because it is the direct object of показала, so it is in the accusative case.

However, for an inanimate masculine noun like эскиз, the accusative singular looks exactly like the nominative singular:

• nominative: простой эскиз
• accusative: простой эскиз

So even though this is the object, the form does not change.

Also, the adjective простой matches эскиз in:

• gender: masculine
• number: singular
• case: accusative (same form here as nominative because it is inanimate)

For the same reason as эскиз: мольберт is an inanimate masculine noun.

After поставила, it is the direct object, so it is accusative. But for inanimate masculine singular nouns, accusative = nominative:

• nominative: мольберт
• accusative: мольберт

So the form stays the same.

If it were an animate masculine noun, you would usually see a different accusative form.

Because рядом с is a fixed prepositional pattern meaning next to or beside, and it requires the instrumental case.

So:

• рядом с кем?
• рядом с чем?

Here the noun is окно, and in the instrumental singular it becomes окном:

• nominative: окно
• instrumental: окном

So:

• рядом с окном = next to the window

This is something you largely memorize with the preposition:

• с братом
• с машиной
• с окном

It means first ... and then ...

In this sentence, it marks the sequence of actions:

1. Сначала учительница показала нам простой эскиз
2. а потом поставила мольберт рядом с окном

So the teacher first showed the sketch, and after that placed the easel by the window.

A useful nuance:

• сначала = at first / first
• потом = then / afterward
• а потом often feels like and then / and after that, with a slight sense of moving on to the next step

In Russian, а is not only but. It can also connect two clauses by shifting from one action or situation to another.

Here, а потом means something like:

• and then
• and after that

It sounds very natural in narration when describing one step followed by another.

So:

• Сначала ..., а потом ... = a common pattern for first ..., then ...

Using и потом is sometimes possible in other contexts, but сначала ..., а потом ... is the standard pairing here.

Because the sentence describes completed actions in sequence.

• показала = showed (completed act)
• поставила = placed / set down (completed act)

The teacher did two finished things:

1. she showed the sketch
2. she placed the easel near the window

If you used imperfective verbs, the meaning would shift more toward process, repetition, or background action.

For example:

• показывала could suggest was showing or used to show
• ставила could suggest was placing or used to place

But here the story is about specific completed events, so perfective is the natural choice.

Yes. Russian word order is more flexible than English because case endings show grammatical roles.

The original sentence is neutral and natural:

• Сначала учительница показала нам простой эскиз, а потом поставила мольберт рядом с окном.

But other orders are possible, depending on emphasis. For example:

• Сначала нам учительница показала простой эскиз...
  This puts a little more focus on to us.

• Мольберт учительница потом поставила рядом с окном.
  This gives more prominence to мольберт.

Still, the original version is probably the best standard order for a learner.

Because both actions have the same subject, and Russian often omits the repeated subject in the second clause when it is obvious.

So this:

• Сначала учительница показала нам простой эскиз, а потом поставила мольберт рядом с окном.

really means:

• Сначала учительница показала нам простой эскиз, а потом учительница поставила мольберт рядом с окном.

But repeating учительница would sound unnecessary.

English does the same thing:

• The teacher first showed us a simple sketch and then placed the easel next to the window.

Yes, эскиз means sketch and is a masculine inanimate noun.

Its basic singular pattern is:

• nominative: эскиз
• genitive: эскиза
• dative: эскизу
• accusative: эскиз
• instrumental: эскизом
• prepositional: об эскизе

In this sentence, it is accusative singular as the thing being shown.

Because it comes from окно, which is singular window.

• окно = window
• окна = windows / also a singular form in some other cases, depending on context
• окном = by/with the window, instrumental singular
• окнами = by/with the windows, instrumental plural

So рядом с окном clearly means next to the window, singular.

No. Here поставила means placed, set, or put.

Russian поставить usually means to place something in a position.

So:

• поставила мольберт рядом с окном = she placed the easel next to the window

If you wanted stood, you would normally use a different verb, such as a form of стоять:

• Мольберт стоял рядом с окном. = The easel stood / was standing next to the window.