Až přijede babička z nemocnice, připravím jí polštář a deku v pokoji.

Because both verbs are perfective:

• přijet = to arrive, as a completed event
• připravit = to prepare, as a completed event

In Czech, the present forms of perfective verbs usually express future meaning:

• přijede = she will arrive
• připravím = I will prepare

So this is completely normal Czech. If you wanted an imperfective idea such as an ongoing process, you would use a different verb and a different future form.

Here až means when / once in the sense of a future point in time.

It suggests this sequence:

1. Grandma arrives.
2. Then I prepare the pillow and blanket.

For a single future event, až is the most natural choice.

Compare:

• Až přijede... = When / Once she arrives...
• Když přijede... can sometimes be heard, but když is more often associated with when/whenever in a general or repeated sense.

So až is a very typical word here.

Czech often drops subject pronouns when the verb ending already makes the subject clear.

In připravím, the ending -ím already tells you the subject is I.

So:

• připravím = I will prepare

You could say Já jí připravím..., but that would add emphasis, something like I will prepare it for her.

Jí is dative singular, meaning to her or for her.

Here it marks the person who benefits from the action:

• připravím jí polštář a deku = I’ll prepare a pillow and a blanket for her

By contrast:

• ji is usually accusative, meaning her as a direct object

So:

• jí = indirect object / recipient / beneficiary
• ji = direct object

In this sentence, the direct objects are polštář a deku, not grandma.

Both are accusative singular, because they are the direct objects of připravím.

• polštář is a masculine inanimate noun
• deka is a feminine noun

Their accusative forms behave differently:

• polštář → polštář
  The accusative is the same as the nominative.
• deka → deku
  Feminine nouns of this type change -a to -u in the accusative singular.

So even though the forms look different, both nouns are doing the same job in the sentence.

The preposition z means from / out of, and it takes the genitive case.

So:

• z nemocnice = from the hospital

A useful detail: the noun nemocnice has the same form in nominative singular and genitive singular, so you do not see a visible ending change here.

Also, Czech has no articles, so there is no separate word for the.

Because v meaning in takes the locative case when it expresses a location.

• pokoj = room
• v pokoji = in the room

So the noun changes to the locative form.

This is different from movement:

• v pokoji = in the room, being there
• do pokoje = into the room, movement toward it

Here the meaning is location, so v pokoji is correct.

Grammatically, v pokoji most naturally means in the room and can be understood as the location connected with the preparing/placing of the pillow and blanket.

In real use, context usually makes it clear. But yes, there is a little room for interpretation in isolation.

If you wanted to be more specific, you could say for example:

• v jejím pokoji = in her room
• do pokoje = into the room

So the original sentence is natural, but not maximally specific.

Yes. Czech word order is fairly flexible because cases show the grammatical roles.

The given sentence is a natural, neutral order:

• time clause first: Až přijede babička z nemocnice
• then the main clause: připravím jí polštář a deku v pokoji

A few things to notice:

• jí is a short pronoun, so it usually stays near the beginning of its clause
• v pokoji can move around depending on emphasis

For example, you could also say:

• V pokoji jí připravím polštář a deku.
• Polštář a deku jí připravím v pokoji.

The meaning stays similar, but the emphasis changes.

Babička is the normal everyday word for grandmother / grandma.

For many learners, it feels closer in tone to grandma than to very formal grandmother.

It is warm and natural, not strange or childish. In ordinary conversation, babička is exactly what you would expect.

Because Až přijede babička z nemocnice is a subordinate clause, and Czech separates subordinate clauses with commas.

So the structure is:

• subordinate clause: Až přijede babička z nemocnice
• main clause: připravím jí polštář a deku v pokoji

That is why the comma is required.