Remélem, hogy holnap visszavihetem a kávéfőzőt a csomagolással.

Because Hungarian usually treats the hogy-clause here as if there were an implied object: (azt) remélem, hogy... = I hope that...

So remélem is the definite 1st person singular form of remél.
A native-speaker way to think of it is:

• Remélem = I hope it / I hope that...
• Remélek = the indefinite form, which is not the normal choice in this sentence

So Remélem, hogy... is the expected wording.

Yes. hogy introduces a subordinate clause, very much like English that:

• Remélem, hogy holnap... = I hope that tomorrow...

In English, that is often optional. In Hungarian, hogy is very common and natural here. In casual speech it can sometimes be omitted, but keeping it is standard and clear.

visszavihetem can be broken down like this:

• vissza = back
• vihet = can/may take, carry
• -em = I (1st person singular definite ending)

So the whole word means roughly:

I can/may take back

In context, that becomes something like I can return / take back.

Because vinni is an irregular verb.

Its forms do not all look the same:

• dictionary form: vinni = to take, carry
• another common form: visz = he/she takes
• potential form: vihet = he/she can take
• here: vihetem = I can take it

So this is just one of those verbs whose stem changes in different forms. That is normal Hungarian behavior for a small group of common verbs.

Because vissza- is a verbal prefix (often called a preverb), and when it stands directly in front of the verb, it is written together with it:

• visszavihetem = I can take back

This prefix often separates in other sentence types, especially with negation or focus. For example:

• Nem vihetem vissza a kávéfőzőt. = I can’t take the coffee maker back.

So in your sentence, the one-word form is the normal neutral pattern.

Because -t marks the direct object in Hungarian.

Here, the coffee maker is the thing being taken back, so it gets the accusative ending:

• kávéfőző = coffee maker
• kávéfőzőt = coffee maker (as direct object)

Since the noun already ends in a vowel, Hungarian just adds -t directly.

Because the sentence has a definite direct object:

• a kávéfőzőt = the coffee maker

Hungarian verbs often agree with whether the object is definite or indefinite.

So:

• vihetem = I can take it / the specific thing
• vihetek = I can take something / an unspecified thing

That is why visszavihetem a kávéfőzőt is the correct match.

a csomagolással means with the packaging.

The ending is the Hungarian -val / -vel case, which often means with.

Here:

• csomagolás = packaging
• csomagolással = with the packaging

Why not csomagolásval? Because Hungarian changes the ending by assimilation:

• after a final s, the v disappears and the following sound doubles
• so -val becomes -sal / -ssal in pronunciation/spelling

That is why you get csomagolással.

Yes. a csomagolásával means with its packaging and is a bit more explicit.

Compare:

• a csomagolással = with the packaging
• a csomagolásával = with its packaging

In many real situations, both can work. The version with the possessive ending can sound a little more precise if you want to emphasize that it is the coffee maker’s own packaging.

Because holnap is already a complete time adverb meaning tomorrow.

Hungarian often uses bare time words without any preposition:

• ma = today
• holnap = tomorrow
• tegnap = yesterday

So holnap alone is exactly what Hungarian needs here.

Hungarian word order is flexible, but different orders change the focus or emphasis.

This sentence has a fairly neutral structure:

Remélem, hogy holnap visszavihetem a kávéfőzőt a csomagolással.

That sounds like a normal statement of hope, with holnap setting the time.

You could move things around, but then you highlight different parts. For example:

• Holnap remélem, hogy visszavihetem... = stronger emphasis on tomorrow
• A csomagolással visszavihetem... = stronger emphasis on with the packaging

So the current order is natural and neutral, not the only possible order.

It can cover all of those, depending on context.

The Hungarian -hat / -het ending can express:

• ability = can
• possibility = can
• permission = may / be allowed to

In this sentence, especially in a return-to-store context, it often suggests something like:

I hope I’ll be allowed to take the coffee maker back tomorrow.

So English may translate it as can, may, or be allowed to, depending on what you want to emphasize.