Moje babička se usmála, když jsme byli všichni doma.

Because the verb is usmát se, which means to smile in the sense of to give a smile / to smile once.
The se is part of the verb itself, not a separate word with a separate meaning here.

So:

• usmát se = to smile
• usmála se = she smiled

Many Czech verbs are learned together with se or si, and this is one of them.

This is mainly a matter of aspect and meaning.

• usmála se is from usmát se and usually means she smiled as a single completed action
• smála se is from smát se and means she was laughing or she laughed, often with a more ongoing sense

So in this sentence, usmála se suggests a brief, completed smile, which fits very naturally.

Because the subject babička is feminine singular.

In the Czech past tense, the main verb form agrees with the subject in gender and number:

• usmál se = he smiled
• usmála se = she smiled
• usmálo se = it smiled
• usmáli se / usmály se = they smiled

Since babička means grandmother and is feminine, the correct form is usmála.

Because Czech often drops subject pronouns when they are not needed.

The word jsme already shows we, so Czech does not need to say my here.

• když jsme byli = when we were
• když my jsme byli = possible, but more emphatic or contrastive

This is very common in Czech. English usually needs the subject pronoun, but Czech often does not.

This is the Czech past tense of být = to be.

Czech past tense is built with:

• an auxiliary form of být
• plus a past participle

Here:

• jsme = auxiliary for we
• byli = past participle

So:

• jsem byl/byla = I was
• jsi byl/byla = you were
• jsme byli/byly = we were

Together, jsme byli means we were.

Because Czech uses the masculine plural form when a group is:

• mixed male and female, or
• includes at least one male, or
• sometimes left unspecified in a general way

So:

• všichni = all of us / everyone, masculine or mixed
• byli = were, masculine or mixed plural

If the group were all female, you would normally say:

• když jsme byly všechny doma

So this sentence suggests that the group was either mixed or not specifically all-female.

For the same reason as byli: the form matches the gender of the group.

• všichni = masculine animate plural, also used for mixed groups
• všechny = feminine plural, or non-masculine plural in some contexts

Here the speaker uses všichni, so the group is being treated as mixed or masculine-type plural.

Because doma means at home, which is the natural expression here.

• doma = at home
• v domě = in the house / inside the building

These are not always interchangeable.

For example:

• Jsme doma. = We are at home.
• Jsme v domě. = We are in the house.

The sentence is about everyone being at home, not just physically inside a building, so doma is the normal choice.

Because když introduces a subordinate clause.

The sentence has:

• main clause: Moje babička se usmála
• subordinate clause: když jsme byli všichni doma

In Czech, subordinate clauses are normally separated by commas, so the comma here is required.

Yes, Czech word order is fairly flexible, but changing it can change the emphasis.

The given sentence is very natural:

• Moje babička se usmála, když jsme byli všichni doma.

You could also hear:

• Moje babička se usmála, když jsme byli doma všichni.

Both are grammatical, but the focus shifts slightly.
The original version sounds neutral and smooth.
The version with všichni later can put more emphasis on everyone.

So the word order is not completely fixed, but the original is a very normal choice.

Both are possible.

• moje babička
• má babička

Both mean my grandmother.

In modern Czech, moje often sounds a bit more natural in everyday speech, while má can sound a little shorter, sometimes slightly more literary or stylistically marked, depending on context. But both are correct, and native speakers use both.

So there is nothing unusual about moje babička here.