Το ξύπνημα στις έξι δεν μου αρέσει, αλλά με βοηθάει να πηγαίνω ήρεμα στη δουλειά.

Το ξύπνημα is a noun, literally the waking up / the act of waking up. Greek often uses an article + noun to talk about an action in a general way.

So:

• Το ξύπνημα στις έξι = Waking up at six

A more verbal alternative would be:

• Το να ξυπνάω στις έξι

Both can work, but το ξύπνημα sounds compact and natural here.

Yes, very often it works that way. In this sentence, το ξύπνημα functions a lot like English waking up.

Greek does not use an -ing form in the same way English does, so it often uses:

• a noun, like το ξύπνημα
• or το να + verb, like το να ξυπνάω

So for an English speaker, το ξύπνημα is a good equivalent of a gerund here.

Στις is the contraction of σε τις.

For clock times, Greek normally uses σε + the article:

• στη μία = at one
• στις δύο = at two
• στις έξι = at six

So στις έξι is simply the normal way to say at six o’clock.

Greek expresses I like / I don’t like differently from English.

Literally, μου αρέσει means something like:

• it is pleasing to me

So:

• δεν μου αρέσει το ξύπνημα στις έξι = I don’t like waking up at six

The thing liked is the grammatical subject, and the person who experiences the liking appears as μου (to me).

Because the two verbs take different kinds of objects.

• αρέσει works like is pleasing to
  • μου = to me
• βοηθάει means helps
  • με = me

So:

• δεν μου αρέσει = I don’t like it
• με βοηθάει = it helps me

This is a very common thing to notice in Greek: different verbs require different cases/pronoun forms.

Because the subject is το ξύπνημα, which is singular neuter.

Even though waking up at six may feel like a whole activity in English, in Greek the core subject is still the singular noun ξύπνημα.

So:

• Το ξύπνημα ... δεν μου αρέσει
• not αρέσουν

If the subject were plural, then the verb would be plural:

• Οι αλλαγές δεν μου αρέσουν = I don’t like the changes

Yes. Both βοηθάει and βοηθά are acceptable forms of he/she/it helps in Modern Greek.

So these are both possible:

• με βοηθάει
• με βοηθά

Βοηθάει is very common in everyday speech and writing. A learner will often see both forms with many verbs of this type.

Because πηγαίνω here is the imperfective form, which matches a repeated or habitual action.

The idea is not helping me go once, but helping me go calmly to work in general / every day.

• να πηγαίνω = to keep going / to go regularly / habitually
• να πάω = to go once, on a specific occasion

So in this sentence, να πηγαίνω is the natural choice.

Να introduces a subordinate verb clause. After verbs like θέλω, μπορώ, πρέπει, βοηθάω, Greek usually uses να + verb.

Here:

• με βοηθάει να πηγαίνω = it helps me to go / it helps me go

So να is not exactly the same as English to, but in many sentences that is the closest translation.

Because ήρεμα is being used adverbially: it describes how the person goes to work.

• ήρεμος / ήρεμη / ήρεμο = calm, as an adjective
• ήρεμα = calmly, as an adverbial form

So:

• πηγαίνω ήρεμα = I go calmly

This is why the form does not match a noun in gender; it is modifying the verb, not a noun.

Greek uses the article with nouns much more often than English does.

• στη δουλειά = literally to the work / to the job
• but in natural English, this is usually just to work

Also, στη is a contraction of σε + τη.

So:

• στη δουλειά = to work

This is very normal Greek usage, and English speakers should not expect article use to match English exactly.