Az újrahasznosítás is fontos.

No. In Az újrahasznosítás is fontos, is does not mean the English verb is.

Here, is is a little particle meaning also, too, or sometimes even.

So this sentence means something like:

• Recycling is also important.
• Recycling too is important.

The word meaning English is is not this is.

In this kind of sentence, Hungarian usually leaves it out.

With a 3rd person singular present-tense sentence like X is important, Hungarian normally does not use van.

So:

• Az újrahasznosítás fontos. = Recycling is important.
• Az újrahasznosítás is fontos. = Recycling is also important.

This is very normal Hungarian. English needs is, but Hungarian often does not in this pattern.

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

Since újrahasznosítás begins with the vowel ú, the correct article is az:

• az újrahasznosítás

Compare:

• a könyv = the book
• az alma = the apple

Hungarian often uses the definite article with abstract nouns or general concepts in places where English does not.

So English says:

• Recycling is important

but Hungarian naturally says:

• Az újrahasznosítás fontos

This does not necessarily mean the recycling in a very specific sense. It can still mean recycling as a general concept.

It is a noun meaning recycling.

It is built from smaller parts:

• újra = again, re-
• hasznosít = make useful / utilize
• -ás / -és = a suffix that turns a verb into an action noun

So újrahasznosítás is basically the act/process of making something useful again, i.e. recycling.

Because is usually goes right after the word or phrase it applies to.

Here it applies to az újrahasznosítás:

• Az újrahasznosítás is fontos.

This means recycling too is important.

So a useful rule is:

• is follows the thing that is being added as also/too

Compare:

• Péter is itt van. = Peter is here too.
• Ez is fontos. = This is important too.

Usually not if you mean recycling too is important.

In your sentence, is belongs with az újrahasznosítás, so it goes after that phrase:

• Az újrahasznosítás is fontos.

If you put is after fontos, it would suggest that important is the thing being added, which is a different structure and usually needs a different context.

So for this meaning, the original sentence is the natural choice.

This order is the most straightforward and natural one for the meaning Recycling is also important.

Hungarian word order is more flexible than English, but word order often shows focus and emphasis.

In this sentence:

• Az újrahasznosítás is = the topic / what we are talking about
• fontos = the comment / new information

If you change the order, you may change the emphasis, not just the style.

Because the subject here is singular: az újrahasznosítás = recycling.

So the predicate adjective is singular too:

• fontos = important

If the subject were plural, Hungarian would normally use a plural form:

• A szabályok fontosak. = The rules are important.

Also, Hungarian does not have grammatical gender, so you do not need different forms for masculine/feminine/neuter.

A rough guide:

• új sounds something like ooj
• sz sounds like English s
• s sounds like English sh
• í is a long ee
• á is a long a sound

So újrahasznosítás is roughly:

• OOY-rah-hahs-no-shee-taash

A few important spelling/pronunciation points:

• s = sh
• sz = s
• stress is normally on the first syllable of the word

So the stress is on ÚJ in újrahasznosítás.

In standard, natural Hungarian, Az újrahasznosítás is fontos is the better form.

Leaving out the article can sound unnatural here, unless you are using a special style such as a headline, a note, or a very compressed expression.

So as a learner, it is safest to use:

• Az újrahasznosítás is fontos.