Перед выходом она поправила шляпу и улыбнулась.

Выходом is in the instrumental case. The preposition перед often takes the instrumental when it means before or in front of.

So:

• выход = exit / leaving
• перед выходом = before leaving / before going out

This is a very common pattern in Russian:

• перед уроком = before class
• перед сном = before sleep / before going to bed

Here выход does not mean a physical exit door so much as the act of going out or leaving.

So перед выходом is best understood as:

• before leaving
• before going out

Depending on context, it could also suggest on her way out.

Поправить is the infinitive: to adjust / to fix / to straighten.

Поправила is the past tense form, and it agrees with она:

• поправил = he adjusted
• поправила = she adjusted
• поправило = it adjusted
• поправили = they adjusted

So она поправила means she adjusted.

In the Russian past tense, verbs show gender in the singular.

Because the subject is она (she), the verb takes the feminine singular ending:

• masculine: -л
• feminine: -ла
• neuter: -ло
• plural: -ли

So:

• она поправила
• она улыбнулась

Both verbs are feminine singular because the subject is она.

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

The dictionary form is:

• шляпа = hat

But after a verb like поправила (adjusted), Russian uses the accusative:

• поправила шляпу = adjusted her hat

For many feminine nouns ending in -а, the accusative singular changes to -у:

• книга → книгу
• мама → маму
• шляпа → шляпу

It usually means she adjusted her hat, straightened her hat, or set her hat right.

The verb поправить often means making something sit properly or look neater, especially with:

• clothes
• hair
• glasses
• a hat

So this is not necessarily repaired the hat. It is more likely a small physical adjustment.

The verb is улыбнуться = to smile.

It is a reflexive verb, marked by -ся or -сь. In this form:

• улыбнуться = to smile
• улыбнулась = she smiled

In modern Russian, улыбнуться is simply the normal verb for smile. You do not need to think of it as literally reflexive in English.

The -сь here is just the reflexive marker attached after a vowel-ending form:

• улыбнулась not
• улыбнула

Both поправила and улыбнулась are perfective past forms. That means the actions are seen as completed single actions:

• she adjusted her hat
• she smiled

This fits the sentence well because it describes a short sequence of finished actions before leaving.

If the sentence used imperfective forms, it would sound more like an ongoing or repeated situation, which would change the feel.

There is no comma because и connects two verbs with the same subject:

• она поправила шляпу
• (она) улыбнулась

This is one simple sentence with two coordinated actions, so no comma is needed.

A comma would usually appear if there were separate clauses with different structure or added complexity.

Yes. Russian word order is fairly flexible.

This sentence starts with the time phrase:

• Перед выходом она поправила шляпу и улыбнулась.

That is a very natural way to set the scene first: Before leaving...

Other word orders are possible, for example:

• Она перед выходом поправила шляпу и улыбнулась.

This still means the same thing, but the emphasis shifts slightly. Russian often changes word order for focus, rhythm, or style rather than basic grammar.