Πριν υπογράψω, θέλω να ρωτήσω τον ιδιοκτήτη αν το νερό και το ίντερνετ είναι μέσα στην τιμή.

Υπογράψω is the aorist subjunctive, first person singular, of υπογράφω.

A very important point for English speakers: aorist in Greek does not automatically mean past.
Here it refers to a single complete action: sign.

So Πριν υπογράψω means before I sign, not before I signed.

Why aorist? Because signing is viewed as one whole event. If Greek wanted to emphasize an ongoing or repeated action, it would normally use a different aspect.

After θέλω, Greek normally uses να + subjunctive.

So:

• θέλω να ρωτήσω = I want to ask

This is one of the most basic patterns in Greek:

• θέλω να πάω = I want to go
• θέλω να δω = I want to see
• θέλω να μιλήσω = I want to speak

You cannot normally leave out να here.

Also, ρωτήσω is again aorist subjunctive, because the speaker wants to perform one complete act of asking.

With πριν, Greek very often uses the subjunctive without να:

• Πριν φύγω
• Πριν κοιμηθείς
• Πριν υπογράψω

So πριν itself is enough to introduce that kind of clause.

You may also hear πριν να in some contexts, but πριν υπογράψω is completely normal and standard.

So the pattern here is:

• πριν + subjunctive = before + verb

Because ιδιοκτήτη is the accusative form, used here as the direct object of ρωτήσω.

The dictionary form is:

• ο ιδιοκτήτης = the owner / landlord

But after ρωτάω / ρωτήσω when the person is the object, Greek uses the accusative:

• ρωτάω τον ιδιοκτήτη = I ask the landlord

So:

• nominative: ο ιδιοκτήτης
• accusative: τον ιδιοκτήτη

This is a very common Greek pattern: articles and nouns change form depending on their role in the sentence.

Here αν means if / whether in an indirect yes-no question.

So:

• ρωτήσω τον ιδιοκτήτη αν... = ask the landlord if / whether...

It does not mean a condition here in the sense of if this happens, then...
Instead, it introduces the content of the question:

• Is water included?
• Is internet included?

Greek uses αν very naturally for this kind of indirect question.

Because both nouns are neuter singular, so they take το in the nominative/accusative singular.

• το νερό
• το ίντερνετ

Also, Greek uses the definite article more often than English.
In English, you might say water and internet, but Greek naturally says the water and the internet, especially when talking about services connected to a rental.

So in context, these mean something like:

• the water service
• the internet service

This is a good question because είναι looks the same for both third person singular and third person plural.

So:

• το νερό είναι = the water is
• το νερό και το ίντερνετ είναι = the water and the internet are

In this sentence, the subject is a combination of two nouns:

• το νερό και το ίντερνετ

So in meaning it is plural, even though the verb form είναι does not change.

English shows the difference clearly with is / are, but Modern Greek does not here.

Literally, it is something like inside the price, but idiomatically it means:

• included in the price
• covered by the price

So:

• είναι μέσα στην τιμή = it is included in the price

This is a very common everyday expression, especially for rentals, hotels, bills, and services.

You can think of it as Greek’s natural way to say that something is part of what you are already paying for.

Στην is a contraction of:

• σε + την → στην

So:

• σε την τιμή becomes στην τιμή

This is extremely common in Greek:

• σε το → στο
• σε την → στην
• σε τον → στον

Also, after the preposition σε, the noun is in the accusative, which is why we get:

• η τιμή = the price
• την τιμή = the price (accusative)

So μέσα στην τιμή is literally inside/in the price.

Yes, Greek word order is fairly flexible, but the original sentence sounds very natural.

The version given:

• Πριν υπογράψω, θέλω να ρωτήσω τον ιδιοκτήτη αν...

puts the time idea first: Before I sign...

You could also say something like:

• Θέλω να ρωτήσω τον ιδιοκτήτη, πριν υπογράψω, αν...

That is still understandable, but the emphasis changes a bit.

So the answer is:

• yes, word order can move
• but the original version is clear and idiomatic

Usually ίντερνετ is treated as an indeclinable neuter loanword in everyday Greek.

That means the noun itself often stays the same, while the article shows the grammar:

• το ίντερνετ
• του ίντερνετ
• στο ίντερνετ

So even if the noun does not visibly change much, Greek still marks case through the article and surrounding words.

This is common with many modern borrowed words.