Varausvahvistuksessa lukee, että lentolippu sisältää vain yhden käsimatkatavaran.

It is the noun varausvahvistus meaning booking confirmation, plus the inessive case ending -ssa, which means in.

So:

• varausvahvistus = booking confirmation
• varausvahvistuksessa = in the booking confirmation

A useful extra detail: many Finnish nouns ending in -us change their stem before case endings:

• vahvistus
• stem: vahvistukse-
• vahvistuksessa

The same happens in the compound varausvahvistus → varausvahvistuksessa.

Yes, lukee is from lukea, which usually means to read, but in this kind of sentence it is often used idiomatically to mean it says / it is written.

So Varausvahvistuksessa lukee, että... is a very natural Finnish way to say:

• It says in the booking confirmation that...
• more literally: In the booking confirmation, it reads that...

It does not mean that someone is reading the confirmation right now.

This is a good question, because it feels different from English.

In Finnish, expressions like jossakin lukee, että... are common and idiomatic. You do not need an obvious subject like English it. The sentence works more like:

• In the booking confirmation, it says that...

So the important idea is not who says it, but where the information appears.

Että means that and introduces a subordinate clause.

Here it connects the two parts:

• Varausvahvistuksessa lukee = it says in the booking confirmation
• että lentolippu sisältää vain yhden käsimatkatavaran = that the plane ticket includes only one carry-on item

So että works just like English that in a sentence such as It says that...

Because lentolippu is the subject of the clause lentolippu sisältää...

In Finnish, the subject is normally in the nominative case, so:

• lentolippu = the plane ticket / a plane ticket

If it were an object instead, the case could change, but here it is the thing that contains/includes, so nominative is correct.

Sisältää is the 3rd person singular form of sisältää = to include / contain.

It is in 3rd person singular because its subject is singular:

• lentolippu sisältää = the ticket includes

This is very normal Finnish agreement:

• lippu sisältää = the ticket includes
• liput sisältävät = the tickets include

Because this phrase is the object of sisältää.

In an affirmative sentence, a complete singular object often appears in the genitive/accusative-looking form:

• yhden käsimatkatavaran

So here the ticket includes one whole carry-on item, and the object is marked accordingly.

Also, yksi is special among numerals: it behaves much more like an adjective and agrees with the noun:

• nominative: yksi käsimatkatavara
• genitive/accusative-type object form: yhden käsimatkatavaran
• partitive: yhtä käsimatkatavaraa

That is why both words change here.

Because yksi behaves differently from numbers 2 and up.

Compare:

• yksi käsimatkatavara = one carry-on item
• kaksi käsimatkatavaraa = two carry-on items

With kaksi, kolme, neljä, etc., the noun is usually singular partitive:

• kaksi käsimatkatavaraa

But with yksi, the noun agrees with the numeral:

• yksi käsimatkatavara
• yhden käsimatkatavaran

So yksi is a bit more adjective-like than the other numerals.

Vain means only and here it limits the quantity:

• vain yhden käsimatkatavaran = only one carry-on item

Its position before the number makes that very clear. The focus is on the restriction: not two, not more, just one.

It means carry-on luggage / hand luggage.

It is a compound noun:

• käsi = hand
• matka = trip / travel
• tavara = stuff, goods, belongings

But in practice, you should learn käsimatkatavara as a whole word meaning carry-on bag / cabin baggage / hand luggage item.

Finnish uses compound nouns very heavily, so long words like this are extremely common.

Because Finnish has no articles.

So Finnish does not normally have separate words corresponding to English a/an and the. Whether something is definite or indefinite is understood from context.

For example:

• lentolippu can mean a plane ticket or the plane ticket
• varausvahvistuksessa can mean in a booking confirmation or in the booking confirmation

In this sentence, the context makes the meaning clear.

Yes. Finnish word order is fairly flexible, and the same idea can be expressed in other natural ways, for example:

• Varausvahvistuksen mukaan lentolippu sisältää vain yhden käsimatkatavaran.
• Lentolippu sisältää varausvahvistuksen mukaan vain yhden käsimatkatavaran.

These all mean roughly the same thing, but the original sentence is very natural because Varausvahvistuksessa lukee, että... is a common way to introduce written information.

Not usually. It sounds less natural, because a booking confirmation does not literally speak.

Finnish prefers expressions like:

• Varausvahvistuksessa lukee, että... = It says in the booking confirmation that...
• Varausvahvistuksessa sanotaan, että... = It is said in the booking confirmation that...
• Varausvahvistuksen mukaan... = According to the booking confirmation...

So lukee is a very idiomatic and natural choice here.