Learn Hardcore Hungarian: Ebédkor a szülők gyakran otthon vannak, és együtt töltenek egy órát a gyerekkel. - At lunchtime the parents are often at home, and they spend an hour together with the child.

szülők by itself would mean “parents” in general, without specifying which ones.
a is the definite article (singular, but also used before plural nouns):
- a szülő – the parent
- a szülők – the parents

In this sentence, we’re talking about a particular set of parents, so Hungarian uses a szülők.

What does gyakran mean, and where can it go in the sentence?

Gyakran means “often / frequently”.

In this sentence:
Ebédkor a szülők gyakran otthon vannak… – At lunchtime the parents are often at home…

Typical positions for gyakran:

A szülők gyakran otthon vannak.
Gyakran otthon vannak a szülők.
Otthon vannak a szülők gyakran. (possible, but this sounds more marked/emphatic)

The neutral, most natural place is usually before the verb or verb phrase, so gyakran otthon vannak works very well.

Why is it otthon vannak and not something like otthonban vannak?

Otthon is an adverb meaning “(at) home”. It does not take a case ending like a regular noun here.

Compare:

otthon vagyok – I am at home
otthon van – he/she is at home
otthon vannak – they are at home

Otthonban is not used in this sense. You just say otthon + a form of lenni (to be) for “to be at home”.

Do we really need vannak in otthon vannak, or could it be omitted?

In many simple present-tense sentences, Hungarian can omit forms of lenni (to be), especially with adjectives and professions:

A szülők otthon. – The parents are at home. (grammatically possible)

However, when the sentence is a bit longer or has more structure (coordination with és, other phrases), Hungarian speakers often keep vannak for clarity and naturalness.

So:

A szülők otthon vannak. – very natural
A szülők otthon. – possible, but sounds more like a short, clipped statement

In the full sentence, otthon vannak is the most natural.

Why is it együtt töltenek and not töltenek együtt?

Both word orders are possible; they just emphasize slightly different things.

…és együtt töltenek egy órát a gyerekkel.
Emphasis is more on being together (“they spend an hour together with the child”).
…és egy órát töltenek együtt a gyerekkel.
A bit more neutral; it sounds like we’re stating “they spend an hour together with the child” in a time-focused way.

Hungarian word order is flexible. Együtt (together) usually goes close to the verb, either before or after it, depending on emphasis. Here, együtt töltenek is very natural.

What does töltenek mean here? Is it literally “to fill”?

The verb tölteni does mean “to fill” in some contexts (e.g. filling a glass).

But it also means “to spend (time)” when used with a time expression:

egy órát tölteni – to spend an hour
sok időt töltök otthon – I spend a lot of time at home

So együtt töltenek egy órát = “they spend an hour together” (not “they fill an hour together” in the literal sense).

Why is egy órát in the accusative (-t)? It’s time, not a direct object, right?

In Hungarian, expressions of duration (how long something lasts) are often put in the accusative:

Egy órát várok. – I wait for an hour.
Két napot dolgoztam. – I worked (for) two days.

So egy órát is in the accusative because it’s a time duration connected to the verb tölteni:
egy órát töltenek – they spend an hour.

What does a gyerekkel mean, and what is the function of -val/-vel?

A gyerekkel means “with the child”.

gyerek – child
-val/-vel – “with” (instrumental/comitative ending)

When you add -val/-vel, consonant assimilation happens:

gyerek + -vel → gyerekkel (k + v becomes kk)

So:

a gyerekkel – with the child
a barátommal – with my friend
a szülőkkel – with the parents

In the sentence, együtt töltenek egy órát a gyerekkel = they spend an hour together with the child. (The idea of “together” is actually doubled: együtt and -val both imply togetherness.)

Is a gyerekkel singular or plural? Does it mean “with the child” or “with the children”?

A gyerekkel is singular: “with the child”.

For plural, you would say:

a gyerekekkel – with the children
(gyerekek + -kel)

If you want to be more explicit that it’s their child:

a gyerekükkel – with their child
a gyerekeikkel – with their children

The given sentence a gyerekkel is context-dependent; often it’s understood as with their child in normal family context, but grammatically it is just “with the child” (singular, definite).

Could we say Ebédidőben instead of Ebédkor? Is there a difference?

Yes, you can say:

Ebédidőben a szülők gyakran otthon vannak…

Ebédidőben = “during lunchtime / at lunchtime”
Ebédkor = “at lunchtime / at the time of lunch”

The difference is subtle:

-kor is more like a point in time.
-ban/ben suggests within a time period.

In everyday speech, both are fine in this context with almost no practical difference.

What tense is this? Is it present simple or something like “usually are at home”?

It’s simple present tense, but in Hungarian the present can naturally express habitual actions (things that happen regularly).

Ebédkor a szülők gyakran otthon vannak…
= At lunchtime the parents are often at home…
→ understood as a habit: they usually/regularly do this.

The adverb gyakran (“often”) gives the habitual meaning that English often expresses with usually / often / regularly in the present simple.