A nyereg és a csengő is új alkatrész.

Because Hungarian usually leaves out the present-tense copula van / vannak in third person when the predicate is a noun or an adjective.

So:

A nyereg és a csengő is új alkatrész.

has no written word for are, but it still means The saddle and the bell are also new parts/components.

This omission is normal in sentences like:

• A ház nagy. = The house is big.
• Péter tanár. = Péter is a teacher.

But Hungarian does use the verb in other situations, for example with location:

• A nyereg és a csengő a dobozban vannak. = The saddle and the bell are in the box.

No. Hungarian is here does not mean is as a verb.

In this sentence, is means also, too, or sometimes even.

So a csengő is means the bell too / the bell also.

This is a very common small Hungarian word, and it comes after the word or phrase it belongs to.

Context decides, but very often in a sentence like this, native speakers understand is as covering the whole coordinated phrase:

A nyereg és a csengő is...
= The saddle and the bell too...

In other words, the whole pair is being added to something already known.

However, because is is attached to the last element, it can also feel especially close to a csengő. If you want to make it completely explicit that both items are individually marked with also, Hungarian can repeat is:

A nyereg is és a csengő is...

So the original sentence is normal, but the exact scope of is depends on context and emphasis.

Because a is the definite article, meaning the, and each noun in the coordination is definite:

• a nyereg = the saddle
• a csengő = the bell

Hungarian usually repeats the article in a phrase like this:

a nyereg és a csengő

That is the normal way to say the saddle and the bell.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since nyereg and csengő both begin with consonant sounds, the correct article is a:

• a nyereg
• a csengő

You would use az before a vowel, for example:

• az autó = the car

This is a very natural question for an English speaker.

In English, you would strongly expect parts. In Hungarian, a singular predicate noun can sometimes be used in a more classifying sense, as if saying that the things mentioned belong to the category new component/part.

So új alkatrész can sound like a category label.

That said, with two separate countable objects, many learners expect the plural, and many native speakers would also find új alkatrészek very natural here.

So:

• új alkatrész = more category-like / classificatory
• új alkatrészek = clearly plural, and often what an English speaker expects

Your instinct to wonder about this is completely reasonable.

Yes, it is one noun phrase:

• új = new
• alkatrész = part / component

Hungarian adjectives normally come before the noun they modify, just like in English:

• új alkatrész = new part
• nagy ház = big house

So in this sentence, új alkatrész is the predicate phrase.

Also note: if the noun were plural, the adjective would still stay unchanged in this position:

• új alkatrészek = new parts

Yes, Hungarian word order is flexible, but changing it usually changes the emphasis.

The original sentence is fairly neutral:

A nyereg és a csengő is új alkatrész.

If you move things around, the sentence may become more contrastive or more strongly focused. Hungarian does this much more than English.

One important rule still holds: is normally stays right after the word or phrase it belongs to.

So learners should usually keep the original order unless they already understand Hungarian focus and emphasis patterns well.

A few sounds here are especially important for English speakers:

• ny is like the ny sound in canyon
• cs is like ch in church
• ő is a long rounded vowel with no exact English equivalent; it is similar to German ö held longer

Very rough approximations:

• nyereg ≈ NYE-reg
• csengő ≈ CHEN-gő

Also, Hungarian stress is normally on the first syllable, so:

• NYE-reg
• CHEN-gő