Reggel a papucs még mindig az ágy mellett van, a párna pedig az ágyon.

They are both the definite article, meaning the.

Hungarian uses:

• a before a consonant
• az before a vowel

So here you get:

• a papucs
• a párna
• az ágy

This is only about pronunciation. It has nothing to do with gender. Hungarian does not have grammatical gender like masculine or feminine nouns.

Reggel means in the morning or simply morning in this sentence.

Hungarian often uses time words as adverbs without adding a preposition like in. So:

• Reggel = in the morning
• Este = in the evening
• Éjjel = at night

That is completely normal Hungarian usage.

Még mindig is a very common way to say still.

The two words together give the idea that the situation has continued and has not changed yet. In this sentence, it means the slipper is still beside the bed.

Very roughly:

• még can mean things like still, yet, more, or even, depending on context
• mindig usually means always

But together, még mindig is a fixed everyday expression meaning still.

So it is best to learn még mindig as a natural phrase.

Grammatically, papucs is singular here, so the verb is also singular:

• a papucs ... van = the slipper is ...

If it were plural, you would normally have:

• a papucsok ... vannak = the slippers are ...

If the English meaning you saw used slippers, that may just reflect how English often talks about this kind of object as a pair. But in the Hungarian sentence itself, the noun is singular.

Hungarian expresses location in more than one way.

1. mellett

This is a postposition, meaning next to / beside.

It comes after the noun:

• az ágy mellett = beside the bed

2. -on

This is a case ending, here meaning on.

It attaches directly to the noun:

• ágy
  • -on = ágyon
• az ágyon = on the bed

So English uses separate prepositions like beside and on, but Hungarian may use either:

• a postposition after the noun
• or a suffix attached to the noun

Pedig links the second part of the sentence to the first and adds a mild contrast or comparison.

Here it means something like:

• while
• whereas
• and as for
• sometimes a soft but

So:

• a párna pedig az ágyon suggests something like and the pillow, on the other hand, is on the bed

It is not a strong contradiction. It just helps compare the two objects and their locations.

The second van is left out because it is understood from the first clause.

The full version would be:

Reggel a papucs még mindig az ágy mellett van, a párna pedig az ágyon van.

Hungarian often omits a repeated verb in the second part of a coordinated sentence when the meaning is obvious.

Important: this is not the same as the general rule where van can disappear in sentences like A ház nagy. In a normal location sentence, you usually do need van:

• A párna az ágyon van.

It is omitted here only because it is repeated and easy to understand.

Yes, the words could be rearranged, but the emphasis would change.

Hungarian word order is much more flexible than English word order. It often shows:

• what the sentence is about
• what is being emphasized
• what information is already known versus new

In this sentence:

• Reggel sets the time frame
• a papucs is the topic
• az ágy mellett gives the location
• van comes at the end in a natural locational sentence pattern

So this order is very normal and natural. A different order might still be grammatical, but it would sound as if you were emphasizing something else.