С промокодом цена стала ниже, и я сразу проверила наличие нужного размера.

Because с here means with, and when с means with, it normally takes the instrumental case.

• промокод → nominative
• с промокодом → instrumental

So С промокодом цена стала ниже literally means With a promo code, the price became lower.

In natural English, this often corresponds to With the promo code or Using the promo code.

Стала comes from стать, which here means to become. So цена стала ниже means the price became lower or ended up lower.

This focuses on a change:

• была ниже = was lower
• стала ниже = became lower

So the sentence is saying that after applying the promo code, the price changed and went down.

Ниже is the comparative form of низкий (low), so цена стала ниже literally means the price became lower.

Russian often prefers short comparative forms like:

• ниже = lower
• выше = higher
• дешевле = cheaper
• лучше = better

All of these are very common.

Could you say дешевле here? Yes:

• С промокодом цена стала дешевле = With the promo code, the price became cheaper

That would also sound natural.
The choice of ниже slightly emphasizes the price level, while дешевле emphasizes cheapness.

Because past tense verbs in Russian agree with the gender of the subject when the subject is singular.

Here the subject is я, and the form проверила tells us the speaker is female.

Compare:

• я проверил = I checked (male speaker)
• я проверила = I checked (female speaker)

So this sentence was said by a woman.

This is about aspect.

• проверила = perfective → a completed action
• проверяла = imperfective → process, repeated action, or background action

Here the meaning is I immediately checked, meaning one completed action. So проверила is the natural choice.

Compare:

• я сразу проверила наличие = I immediately checked the availability
• я проверяла наличие весь вечер = I was checking the availability all evening

Сразу means right away, immediately, or at once.

So я сразу проверила means:

• I checked right away
• I immediately checked

It adds the idea that the speaker did this as soon as the price dropped.

Because наличие means availability / presence, and this noun normally takes the genitive case for the thing that is available.

So:

• наличие товара = availability of the product
• наличие билетов = availability of tickets
• наличие нужного размера = availability of the needed size

Here:

• нужный размер = the needed size
• in genitive: нужного размера

So the speaker checked whether the required size was available.

In practice, it means whether the needed size is available.

Literally, it is closer to availability of the needed size. But in English we would usually say:

• I checked whether they had my size
• I checked the availability of the size I needed
• I checked if the needed size was in stock

So even though the Russian structure is noun-based, the real meaning is about stock availability in that size.

Russian has no articles like a, an, or the.

So цена can mean:

• the price
• a price

And нужного размера can mean:

• the needed size
• a needed size

The exact meaning depends on context. In this sentence, English naturally uses the:

• the price
• the needed size / the right size

The word order is natural, but Russian word order is more flexible than English.

This version puts the context first:

• С промокодом = with the promo code
• then the main statement:
• цена стала ниже = the price became lower

It sounds smooth because it first sets up the condition, then gives the result.

Other word orders are possible, for example:

• Цена с промокодом стала ниже
• Цена стала ниже с промокодом

But the original version is very natural and clear.

Yes, промокод is a very common modern Russian word, especially in online shopping.

It means promo code, discount code, or coupon code.

It is basically a borrowed/modern commercial term, and you will see it often on websites, ads, and marketplaces.

Yes. The original sentence is completely natural, but in everyday speech someone might also say:

• С промокодом цена стала ниже, и я сразу проверила, есть ли нужный размер.
• С промокодом стало дешевле, и я сразу посмотрела, есть ли мой размер.

These versions may sound a bit more conversational:

• есть ли нужный размер = whether the needed size is available
• мой размер = my size
• посмотрела = looked/checked

But the original sentence is still good, natural Russian.