Στο τέλος του μήνα πληρώνουμε τα κοινόχρηστα και ελέγχουμε αν η θέρμανση δουλεύει σωστά.

Στο is the normal contracted form of σε + το in modern Greek.

So:

• σε το τέλος → στο τέλος

This is very common:

• στο = σε + το
• στη / στην = σε + τη / την
• στον = σε + τον
• στα = σε + τα

Here στο τέλος means at/in the end.

Του μήνα is genitive singular, meaning of the month.

The structure is:

• στο τέλος = at the end
• του μήνα = of the month

So literally, it is at the end of the month.

A useful point: the noun μήνας changes form outside the dictionary form.

• nominative: ο μήνας
• genitive: του μήνα
• accusative: τον μήνα

So the final -ς disappears in the genitive and accusative singular.

Because τέλος is a neuter noun, and in the singular its nominative and accusative forms are the same.

Dictionary form:

• το τέλος

After σε, Greek normally uses the accusative, but for many neuter nouns the accusative looks identical to the nominative. So you still see τέλος.

Greek often drops subject pronouns when they are not needed, because the verb ending already shows the subject.

Here:

• πληρώνουμε = we pay
• ελέγχουμε = we check

The ending -ουμε tells you the subject is we.
If you added εμείς, it would usually be for emphasis:

• Εμείς πληρώνουμε... = We pay...

Both are present tense, specifically present indicative:

• πληρώνουμε = we pay
• ελέγχουμε = we check

In Greek, the present is often used for habitual or regular actions, just like in English:

• At the end of the month we pay...
• meaning this is something we normally do

If you wanted a one-time future action, Greek would usually use θα:

• Στο τέλος του μήνα θα πληρώσουμε... = At the end of the month we will pay...

Τα κοινόχρηστα usually means the shared building expenses or common charges, especially in an apartment building.

It comes from the adjective κοινόχρηστος / κοινόχρηστη / κοινόχρηστο, meaning shared or for common use. But in real usage, the neuter plural τα κοινόχρηστα is very often used like a noun.

It can refer to things like:

• stairwell cleaning
• elevator costs
• shared electricity
• maintenance of common areas
• building management fees

So this is a very common everyday housing word in Greek.

It is neuter plural because Greek commonly uses adjectives as nouns, and τα κοινόχρηστα has become a standard set phrase.

Grammatically:

• κοινόχρηστος = masculine singular
• κοινόχρηστη = feminine singular
• κοινόχρηστο = neuter singular
• κοινόχρηστα = neuter plural

Why plural? Because it refers to a group of shared expenses/charges, not just one item.

That is why you get:

• πληρώνουμε τα κοινόχρηστα = we pay the common charges

Here αν means if/whether in the sense of an indirect yes/no question.

So:

• ελέγχουμε αν η θέρμανση δουλεύει σωστά
• = we check whether / if the heating works properly

This is different from ότι or πως, which introduce clauses like that...

Compare:

• Ξέρω ότι δουλεύει. = I know that it works.
• Ελέγχω αν δουλεύει. = I check whether/if it works.

Because after αν in this sentence, Greek uses the indicative, not να.

This clause is an indirect question:

• αν η θέρμανση δουλεύει σωστά = whether the heating is working properly

So δουλεύει is a normal finite verb in the indicative.

Να is used in different kinds of clauses, such as:

• desire
• purpose
• possibility
• commands/subjunctive-style meanings

So after ελέγχουμε αν..., να would not be the normal choice.

Θέρμανση is a feminine noun, so it takes the feminine singular article η.

• η θέρμανση = the heating / the heating system

In this clause, η θέρμανση is the subject of δουλεύει, so it is in the nominative.

That is why the clause is:

• η θέρμανση δουλεύει
• the heating works

In Greek, δουλεύω does not only mean to work in the sense of having a job. It also means to function, to operate, or to be working properly for machines, devices, systems, and utilities.

So Greek naturally says things like:

• Το πλυντήριο δουλεύει. = The washing machine works.
• Το ίντερνετ δεν δουλεύει. = The internet isn’t working.
• Η θέρμανση δουλεύει. = The heating works / is working.

Here δουλεύει is 3rd person singular, matching the singular subject η θέρμανση.

Because σωστά here is an adverb, not an adjective.

It describes how the heating works:

• δουλεύει σωστά = works properly / works correctly

If you used an adjective like σωστή, it would need to describe a noun, not the verb.

Compare:

• Η απάντηση είναι σωστή. = The answer is correct.
  
  • σωστή describes απάντηση
• Η θέρμανση δουλεύει σωστά. = The heating works properly.
  
  • σωστά describes δουλεύει

Yes. Greek word order is more flexible than English, because case endings and verb forms carry a lot of grammatical information.

The given sentence has a very natural, neutral order:

• Στο τέλος του μήνα πληρώνουμε τα κοινόχρηστα και ελέγχουμε αν η θέρμανση δουλεύει σωστά.

But you could also say:

• Πληρώνουμε τα κοινόχρηστα στο τέλος του μήνα και ελέγχουμε αν η θέρμανση δουλεύει σωστά.

This still sounds natural, but the emphasis shifts slightly.
Starting with Στο τέλος του μήνα highlights the time frame first.

So the original order is normal, but not the only possible one.