Auch die Hotelrechnung dient als Kostennachweis.

Here, auch means also or too.

In this sentence, it most naturally applies to die Hotelrechnung, so the sense is:

• The hotel bill also serves as proof of expenses.

That suggests that some other document(s) can serve as proof too, and the hotel bill is being added to that list.

German very often forms compound nouns by joining smaller nouns into one longer noun.

So:

• Hotel = hotel
• Rechnung = bill / invoice

Together:

• die Hotelrechnung = hotel bill / hotel invoice

This is completely normal in German. English often uses separate words where German prefers one compound word.

dient is the 3rd person singular present tense form of the verb dienen.

• dienen = to serve
• dient = serves

It ends in -t because the subject is singular:

• die Hotelrechnung dient = the hotel bill serves

Compare:

• ich diene = I serve
• du dienst = you serve
• er/sie/es dient = he/she/it serves

Because it is the thing that is doing the action of serving as proof.

So in:

• Auch die Hotelrechnung dient als Kostennachweis.

the subject is:

• die Hotelrechnung

That is why the verb is singular: dient, not dienen.

Because German uses als to express a role or function, just like English as.

So:

• als Kostennachweis = as proof of expenses

With dienen, this is a very common pattern:

• etwas dient als ... = something serves as ...

For example:

• Ein Reisepass dient als Ausweis. = A passport serves as ID.
• Die Quittung dient als Nachweis. = The receipt serves as proof.

After als, German often leaves out the article when a noun describes a role, function, or category.

So:

• als Kostennachweis = as proof of expenses

This is similar to other common patterns such as:

• als Lehrer = as a teacher
• als Beispiel = as an example
• als Beweis = as proof

Using no article sounds natural and general here. It is describing what the hotel bill functions as.

Kostennachweis is another compound noun:

• Kosten = costs / expenses
• Nachweis = proof / verification / documentation

So Kostennachweis literally means something like:

• proof of expenses
• documentation of costs

Its gender is masculine:

• der Kostennachweis

A useful rule: in German compound nouns, the last part usually determines the gender. Since der Nachweis is masculine, der Kostennachweis is masculine too.

This is a normal main clause, so the finite verb must be in second position.

The sentence begins with:

• Auch die Hotelrechnung

Then the verb comes second:

• dient

So the structure is:

• Auch die Hotelrechnung | dient | als Kostennachweis

German does not mean “second word” here, but rather second sentence element. The whole phrase Auch die Hotelrechnung counts as the first element.

Yes, but moving auch can slightly change the emphasis.

Compare:

• Auch die Hotelrechnung dient als Kostennachweis.

  • The hotel bill too serves as proof.

• Die Hotelrechnung dient auch als Kostennachweis.

  • The hotel bill serves also as proof of expenses.

Both are possible, but the first version puts the focus more clearly on the hotel bill as an additional acceptable document.