У продавца была маленькая рулетка, и с её помощью мы быстро проверили глубину комода.

Russian usually expresses possession with the pattern у + genitive + быть.

So:

• У продавца была маленькая рулетка
  literally = At the seller there was a small tape measure
• natural English = The seller had a small tape measure

Using иметь is possible in Russian, but in everyday speech this у кого-то есть / был(а/о/и) pattern is much more common and natural.

Because у requires the genitive case when it means at/by someone.

• nominative: продавец = seller
• genitive: продавца = of the seller / at the seller

So у продавца means with the seller, in the seller’s possession, or literally at the seller.

Была is the past tense of быть, and in Russian past tense it agrees with the grammatical gender and number of the subject.

Here, the grammatical subject is маленькая рулетка:

• рулетка is feminine singular
• so the verb is была

Compare:

• был for masculine
• была for feminine
• было for neuter
• были for plural

Even though the sentence is about the seller having something, the noun that controls the verb is рулетка, not продавца.

Because adjectives must agree with the noun they describe in gender, number, and case.

Here:

• рулетка is feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• маленькая рулетка

If the noun were masculine, you would get маленький; if neuter, маленькое; if plural, маленькие.

Yes, рулетка can mean roulette, but in everyday Russian it also very commonly means a tape measure or measuring tape, especially a retractable one.

In this sentence, because they use it to check the depth of a piece of furniture, рулетка clearly means tape measure.

So context decides the meaning.

This is a very common expression meaning with the help of it / using it.

Breakdown:

• с = with
• помощью = help (instrumental form of помощь)
• её = its / her, in the genitive form here

So:

• с её помощью = with its help / using it

In this sentence, её refers back to рулетка, so the whole phrase means using the tape measure.

This expression is extremely common in Russian:

• с помощью компьютера = with the help of a computer
• с помощью друга = with the help of a friend

Because the expression с помощью is followed by the genitive case: с помощью кого? чего?

So the pronoun has to be in the genitive form:

• она = she
• её = her / of her / its

Since рулетка is a feminine noun, the pronoun referring to it is also feminine in form: её.

So literally this is something like with the help of it.

Yes. In normal Russian writing, ё is often written as е.

So you may see either:

• её
• ее

Both mean the same thing here.

However, writing ё is very helpful for learners, because it shows the correct pronunciation and can prevent confusion. In careful teaching materials, dictionaries, and some edited texts, ё is more often written explicitly.

Because проверили is perfective, and it presents the action as completed.

Here the idea is:

• we checked the depth
• and the check was successfully finished

So проверили fits well.

If you used проверяли, that would be imperfective, focusing more on the process, repetition, or ongoing action:

• мы проверяли глубину = we were checking / used to check the depth

In this sentence, the result matters, so проверили is the natural choice.

There are two case choices here:

• глубину is accusative, because it is the direct object of проверили
• комода is genitive, because it means the depth of the chest of drawers

So:

• глубина = depth
• глубину = depth (as a direct object)
• комод = chest of drawers / dresser
• комода = of the chest of drawers

Literally, Russian says checked the depth of the dresser, not checked the dresser’s depth.

No, Russian word order is fairly flexible.

This version is natural and neutral:

• мы быстро проверили глубину комода

But other orders are also possible, with different emphasis:

• мы проверили глубину комода быстро
• быстро мы проверили глубину комода
• глубину комода мы быстро проверили

The basic meaning stays the same, but the emphasis shifts. The sentence you were given sounds like a normal, straightforward narrative order.