Я надела сандалии без каблуков и пошла гулять по набережной.

Because the speaker is female.

In the past tense, Russian verbs agree with gender and number:

• надел = masculine
• надела = feminine
• надело = neuter
• надели = plural

So Я надела... tells you the speaker is a woman.

This is a very common question.

• надеть = to put on an item of clothing
• одеть = to dress someone

So:

• надеть сандалии = to put on sandals
• одеть ребёнка = to dress a child

In this sentence, the speaker put on sandals, so надела is the correct verb.

A common memory trick is:

• надеть что
• одеть кого

Because Russian usually treats sandals as a plural item, just like English often does.

• сандалии = sandals

A singular form сандалия exists, but in normal usage people usually talk about the pair as сандалии.

Also, here сандалии is the direct object of надела, so it is in the accusative. Since it is an inanimate plural noun, the accusative looks the same as the nominative:

• nominative: сандалии
• accusative: сандалии

Because the preposition без always takes the genitive case.

The basic noun is:

• каблук = heel

After без, it becomes:

• без каблуков = without heels

This is genitive plural.

Because the sentence is talking about sandals, and each sandal can have a heel, so Russian naturally uses the plural.

So сандалии без каблуков means sandals without heels.

This is the normal way to say that they are flat or heelless. A singular form such as без каблука would usually sound odd here unless you meant something very specific, like one shoe missing one heel.

More or less, yes.

Literally it means without heels, but in natural English the idea is often flat sandals or sandals with no heels.

So the Russian phrase focuses on the absence of heels, while English might translate it more idiomatically.

Because пойти and идти are different in aspect and meaning.

• шла from идти = was walking / went on foot / walked
• пошла from пойти = set off, went off, started going

In this sentence, the idea is:

1. she put on the sandals
2. she went out for a walk

So пошла fits well because it marks the beginning of that action: she set off.

Also, пошла is feminine past tense, just like надела.

Russian often uses a verb of motion plus an infinitive to show purpose.

So:

• пошла гулять = went to take a walk / went out walking / went for a walk

The infinitive гулять tells you what she went to do.

This is a very common pattern:

• пошёл работать = went to work
• пошли есть = went to eat
• пошла гулять = went out for a walk

Because гулять is treated here as an ongoing activity, not a completed result.

The focus is not on finishing the walk, but on the activity itself: she went out to walk / to stroll.

That is why the imperfective infinitive гулять is natural here.

It is dative singular.

The noun is:

• набережная = embankment, waterfront, promenade

After по, when it means movement along or around a place, Russian uses the dative:

• по набережной = along the embankment / along the waterfront

So:

• nominative: набережная
• dative: набережной

Because they mean different things.

• на набережную = to the embankment, toward it as a destination
• по набережной = along the embankment, moving around on it

In this sentence, the idea is not just that she went to the embankment, but that she walked along it. So по набережной is the right choice.

Compare:

• Я пошла на набережную = I went to the embankment
• Я гуляла по набережной = I walked along the embankment

Because Russian has no articles.

Russian does not have words equivalent to a and the. Whether something is definite or indefinite is understood from context.

So по набережной could mean:

• along the embankment
• along a waterfront promenade

Usually the surrounding context makes it clear which is meant.

Yes, very often.

Russian often drops subject pronouns when the verb form already makes the subject clear. So this could also be:

• Надела сандалии без каблуков и пошла гулять по набережной.

That still clearly means I put on sandals without heels and went for a walk along the embankment, especially in context.

Keeping Я can add a little emphasis, contrast, or simply make the sentence feel more explicit.