Το στρώμα φαίνεται άνετο, αλλά θέλω να πλύνω το σεντόνι πριν κοιμηθώ εκεί απόψε.

Because στρώμα and σεντόνι are both neuter singular nouns.

• το στρώμα = the mattress
• το σεντόνι = the sheet

The adjective άνετο has to agree with στρώμα in gender and number, so it is also neuter singular. That is why you get το στρώμα φαίνεται άνετο and not άνετος or άνετη.

Not quite.

φαίνεται comes from φαίνομαι and means seems, appears, or looks. So:

• Το στρώμα φαίνεται άνετο = The mattress seems/looks comfortable
• Το στρώμα είναι άνετο = The mattress is comfortable

So φαίνεται suggests an impression, not a firm statement of fact.

In Modern Greek, να introduces a dependent verb form, often called the subjunctive.

Greek does not use an infinitive the way English does. So instead of saying I want to wash, Greek says literally something like I want that I wash:

• θέλω να πλύνω = I want to wash

This pattern is extremely common:

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

This is mainly about aspect.

• πλένω = imperfective, more like wash / be washing / wash regularly
• πλύνω = perfective stem, used here for wash once / wash completely

After θέλω να, Greek often chooses between imperfective and perfective depending on how the action is viewed.

Here the speaker wants to do one complete action: wash the sheet before sleeping there. So πλύνω is the natural choice.

A rough contrast:

• Θέλω να πλένω τα σεντόνια κάθε εβδομάδα = I want to wash the sheets every week
• Θέλω να πλύνω το σεντόνι τώρα = I want to wash the sheet now

This is the same aspect idea again.

The basic verb is κοιμάμαι = I sleep / I am sleeping.
Its perfective form is κοιμηθώ, which here means something like go to sleep or fall asleep.

So:

• πριν κοιμηθώ = before I go to sleep
• not the more general before I am sleeping

In English we often just translate this as before I sleep, but the Greek form is more naturally before I go to sleep.

Because πριν can introduce this kind of clause by itself.

So πριν κοιμηθώ is a very natural way to say before I go to sleep.

You may also hear πριν να κοιμηθώ. Both exist, but πριν κοιμηθώ is very common and natural in everyday Greek.

Greek usually leaves subject pronouns out because the verb ending already shows the person.

Here:

• θέλω = I want
• πλύνω = I wash / I want to wash
• κοιμηθώ = I go to sleep

So Greek does not need εγώ unless the speaker wants emphasis or contrast.

• Εγώ θέλω να πλύνω το σεντόνι would sound more like I want to wash the sheet (maybe not someone else).

εκεί means there.

In this sentence it refers to the place associated with the mattress, so να κοιμηθώ εκεί means to sleep there. In natural English, depending on context, that may feel like sleep on it or sleep there on that bed/mattress.

Greek often uses a simple location word like εκεί where English might choose a more specific phrase.

απόψε means tonight.

It is very close in meaning to σήμερα το βράδυ (this evening / tonight), but απόψε is shorter and very common.

So:

• εκεί απόψε = there tonight

Putting απόψε at the end is a normal, natural placement.

Yes.

• το στρώμα is the subject of φαίνεται, so it is in the nominative
• το σεντόνι is the object of πλύνω, so it is in the accusative

But for many neuter singular nouns in Greek, the nominative and accusative have the same form. So the role is understood from the sentence structure, not from a visible ending change.

Yes. Greek word order is more flexible than English word order.

This sentence uses a very natural neutral order:

• Το στρώμα φαίνεται άνετο
• αλλά
• θέλω να πλύνω το σεντόνι πριν κοιμηθώ εκεί απόψε

But some parts could move for emphasis. For example:

• Απόψε θέλω να πλύνω το σεντόνι...
• Θέλω να πλύνω το σεντόνι απόψε...

The original version sounds balanced and natural, with απόψε left until the end to set the time of sleeping.

Because αλλά means but, and it connects two full clauses:

• Το στρώμα φαίνεται άνετο
• θέλω να πλύνω το σεντόνι πριν κοιμηθώ εκεί απόψε

In Greek, as in English, a comma is normally used before αλλά when it joins two contrasting clauses.