Після довгого дня ми обіймаємо одна одну і сміємося.

Because після requires the genitive case.

So:

• довгий → довгого
• день → дня

That gives після довгого дня = after a long day.

This is a very common pattern in Ukrainian: certain prepositions automatically force a specific case, and після is one of the prepositions that takes the genitive.

Yes. Ukrainian often omits subject pronouns when they are clear from the verb ending.

Both verbs already show 1st person plural:

• обіймаємо = we hug / we are hugging
• сміємося = we laugh / we are laughing

So Обіймаємо одна одну і сміємося is also grammatical.

Including ми can add a little emphasis or clarity, but it is not required.

Обіймаємо is present tense, 1st person plural, from the imperfective verb обіймати.

That means it can describe:

• an action happening now: we are hugging
• a usual/repeated action: we hug

The exact English translation depends on context.

The perfective partner is обійняти. A perfective form would not normally be used here for a present ongoing action.

Одна одну is the Ukrainian way to say each other or one another in this kind of sentence.

So:

• обіймаємо одна одну = we hug each other

This construction is very common with reciprocal actions, where the people in the subject do the action to one another.

Because this reciprocal expression is built that way in Ukrainian.

In одна одну:

• одна is nominative singular feminine
• одну is accusative singular feminine

Even though the overall meaning is plural (each other), Ukrainian uses this fixed singular-based pattern.

So it may look strange to an English speaker at first, but it is normal Ukrainian grammar.

Yes. It strongly suggests that ми refers to an all-female group.

Why?

Because одна одну uses the feminine form.

Compare:

• одна одну = used for an all-female group
• один одного = used for an all-male or mixed group

So this sentence sounds like we refers to women or girls.

Yes, absolutely.

• ми обіймаємося = we hug each other / we are hugging
• ми обіймаємо одна одну = also we hug each other

The version with одна одну is more explicit about the reciprocal meaning. It can also sound a bit more emphatic or stylistically fuller.

In everyday speech, обіймаємося is very common.

Because the verb is сміятися, which means to laugh.

So the -ся is part of the verb:

• я сміюся = I laugh / I am laughing
• ми сміємося = we laugh / we are laughing

If you remove -ся, you no longer have the normal verb meaning to laugh.

So сміємося is the correct form here.

In this verb, -ся is part of the verb form inherited from a reflexive pattern, but in modern Ukrainian сміятися simply means to laugh.

So you should learn сміятися as a whole dictionary form, not as сміяти + ся with a separate literal meaning like laugh oneself.

Many Ukrainian verbs work this way:

• сміятися = to laugh
• боятися = to fear / be afraid
• здаватися = to seem

For learners, the safest approach is to memorize such verbs with -ся included.

Yes. Ukrainian word order is fairly flexible.

The given sentence:

• Після довгого дня ми обіймаємо одна одну і сміємося

is a neutral, natural order.

You could also say:

• Ми після довгого дня обіймаємо одна одну і сміємося
• Після довгого дня обіймаємо одна одну і сміємося

These versions are still understandable, but the emphasis shifts slightly.

Ukrainian uses word order more for focus and style than English does, because case endings and verb forms already show many grammatical relationships.

Because і is simply joining two verbs with the same subject:

• обіймаємо
• сміємося

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

It works like English:

• We hug each other and laugh.

You normally would not put a comma there either.

Yes, depending on context.

Ukrainian has no articles, so it does not directly distinguish between:

• a long day
• the long day

The context tells you which meaning is intended.

In most cases, після довгого дня will naturally be understood as after a long day, but a more specific meaning is also possible if the context supports it.