Minä ostan pienen matkamuiston vasta paluumatkalla, mutta Laura ostaa matkamuiston jo lentokentältä.

Yes. Finnish often leaves out subject pronouns because the verb ending already shows the person:

• ostan = I buy / I will buy
• ostaa = he/she buys / will buy

So Ostan pienen matkamuiston... would be perfectly natural.

Here, minä is probably included for emphasis or contrast, especially because the sentence later contrasts I with Laura:

• Minä ostan... mutta Laura ostaa...
• I buy..., but Laura buys...

So minä is not required, but it helps underline the comparison.

Finnish often uses the present tense for future meaning when the context makes the time clear.

So:

• Minä ostan... can mean I buy or I will buy
• Laura ostaa... can mean Laura buys or Laura will buy

Because the sentence talks about buying something on the return trip and from the airport, the future meaning is understood from context.

This is very normal in Finnish.

Because the noun is in the object form here, and the adjective must match it.

The basic dictionary forms are:

• pieni = small
• matkamuisto = souvenir

In this sentence, the speaker is buying one whole souvenir, so Finnish uses the total object form. In the singular, that usually looks like -n:

• matkamuisto → matkamuiston
• pieni → pienen

So:

• pieni matkamuisto = a small souvenir
• pienen matkamuiston = a small souvenir (as a complete object being bought)

The adjective and noun agree in case and number.

Because it is the object of the verb ostaa and refers to a complete, finished item: one whole souvenir.

In Finnish, this is called the total object. In the singular, it often has the same form as the genitive:

• matkamuisto → matkamuiston

So ostan matkamuiston means I am buying / will buy the souvenir, one complete souvenir.

Compare that with a partitive object:

• ostan matkamuistoa

That would sound more like I’m buying some souvenir or I’m souvenir-shopping, with a less complete or less bounded sense.

In this sentence, the idea is clearly one complete souvenir, so matkamuiston is used.

Here vasta means not until or only in the sense of later than you might expect.

So:

• vasta paluumatkalla = not until the return trip

It gives the idea that the speaker is delaying the purchase.

This contrasts with jo later in the sentence:

• vasta = late, not until
• jo = already, as early as

So the sentence sets up a timing contrast:

• I won’t buy one until the return trip
• but Laura buys one already at/from the airport

In this sentence, jo means already or as early as.

So:

• Laura ostaa matkamuiston jo lentokentältä = Laura buys a souvenir already / as early as from the airport

It suggests that Laura buys the souvenir earlier than the speaker does.

Together, vasta and jo create a strong contrast:

• vasta = not until later
• jo = already, early

Because they express different kinds of location or relation.

paluumatkalla

This is the adessive form (-lla/-llä), which often means:

• on
• at
• during

So paluumatkalla means on the return trip or during the return journey.

lentokentältä

This is the ablative form (-lta/-ltä), which often means:

• from
• off
• from the vicinity/surface of

With ostaa, Finnish often uses a source expression for where something is bought from:

• ostaa kaupasta = buy from a shop
• ostaa torilta = buy from the market
• ostaa lentokentältä = buy from the airport

Even if English might say at the airport, Finnish commonly says from the airport in this kind of sentence.

Because the sentence is treating the airport as the source of the purchase, not just the location where Laura happens to be.

• lentokentällä = at the airport
• lentokentältä = from the airport

With ostaa, Finnish very often uses a source case:

• Ostan sen kaupasta = I buy it from the shop
• Ostan sen lentokentältä = I buy it from the airport

So while English often prefers at the airport, Finnish naturally uses lentokentältä in this context.

Yes. It comes from the compound noun:

• paluumatka = return trip / return journey

This itself is made from:

• paluu = return
• matka = trip, journey

Then it is put into the adessive case:

• paluumatka → paluumatkalla

So paluumatkalla literally means something like on the return trip.

Yes.

• matka = trip, travel
• muisto = memory, keepsake

Together:

• matkamuisto = travel souvenir / souvenir

This is a very common kind of Finnish compound formation: two nouns combine into one word.

So Finnish often expresses ideas with one compound word where English uses two separate words.

There is no special grammar reason. The adjective is simply omitted because it is not needed in the second half.

The first half says:

• pienen matkamuiston = a small souvenir

The second half just says:

• matkamuiston = a souvenir

So the sentence does not explicitly say that Laura’s souvenir is small. It may be small too, but the Finnish sentence does not specify that.

This is just a meaning choice, not a grammatical rule.

Yes, Finnish word order is fairly flexible, but this order is natural because it places the timing words right before the phrases they modify:

• vasta paluumatkalla
• jo lentokentältä

This makes the contrast easy to hear:

• not until on the return trip
• already from the airport

You could move words around for emphasis, but the given version is clear and natural.

Because Finnish verbs change according to the subject.

For ostaa (to buy):

• minä ostan = I buy
• sinä ostat = you buy
• hän ostaa = he/she buys

A proper name like Laura takes the same verb form as hän, so:

• Laura ostaa

That is why the sentence has:

• Minä ostan...
• Laura ostaa...

Because mutta means but, and it joins two main clauses:

• Minä ostan pienen matkamuiston vasta paluumatkalla
• mutta Laura ostaa matkamuiston jo lentokentältä

In Finnish, a comma is normally used before mutta when it connects clauses like this. This is similar to standard written English usage before but joining two full clauses.