A saját kezű aláírás és a hozzájárulás fontos.

Because Hungarian normally omits the verb van (is/are) in the present tense, third person when the predicate is a noun or adjective.

So:

• A saját kezű aláírás és a hozzájárulás fontos. = The handwritten signature and the consent are important.

But compare:

• Fontos vagyok. = I am important.
• Fontos volt. = It was important.
• Fontosak. = They are important.

In your sentence, the missing is/are is completely normal.

Saját kezű is a formal expression meaning written or signed by one’s own hand.

Literally, it is something like of one’s own hand, but in natural English it usually means:

• handwritten
• personally signed
• in legal/official contexts, often a physical signature made by the person themselves

So saját kezű aláírás is not just any signature. It suggests a signature personally written by the person, not just a typed name or sometimes not an electronic substitute.

It comes from kéz = hand.

In compounds and derived forms, the stem often appears as kez-, and here it takes the adjectival ending -ű/-ú, which gives a meaning like having / with.

So:

• kéz = hand
• kezű = handed / having a hand of a certain kind

That is why saját kezű literally has the sense of with one’s own hand.

This is a somewhat formal/literary pattern, and in this phrase it is best learned as a set expression.

Hungarian often repeats the definite article before each noun in a coordination when both items are definite and separate:

• a saját kezű aláírás
• a hozzájárulás

So a X és a Y is very normal.

Repeating the article helps show that both nouns are definite and listed as separate items. In formal or administrative language, this is especially common and natural.

Hozzájárulás is a noun formed from the verb hozzájárul.

• hozzájárul = to consent / to give approval / to agree
• hozzájárulás = consent / approval / authorization

The ending -ás/-és is a very common noun-forming suffix in Hungarian.

So this is similar to English pairs like:

• approve → approval
• sign → signing/signature (depending on context)

In official language, hozzájárulás often means consent.

That is a very natural question, because the subject contains two nouns.

In Hungarian, with coordinated subjects, you may see either:

• fontosak = clear plural agreement
• fontos = singular form, often when the two things are treated as one combined requirement or one general issue

So in many contexts:

• A saját kezű aláírás és a hozzájárulás fontosak.
  would also sound natural.

But the singular fontos is also used, especially in formal or administrative wording, where the speaker treats the whole phrase as one combined condition.

So the short answer is: fontos here is not a mistake, even though fontosak is also possible in many situations.

Yes. Hungarian word order is flexible.

You could also say:

• Fontos a saját kezű aláírás és a hozzájárulás.

Both are grammatical, but the emphasis changes a little.

• A saját kezű aláírás és a hozzájárulás fontos.
  The noun phrase is the topic: we are talking about these items, and saying something about them.

• Fontos a saját kezű aláírás és a hozzájárulás.
  This puts more emphasis on important.

So the meaning stays basically the same, but the information structure changes.

Usually, adjectives before nouns do not agree the way they do in many Indo-European languages.

Hungarian has:

• no grammatical gender
• no adjective agreement for gender
• no adjective agreement for number in normal attributive position

So:

• saját
• kezű

do not change to match aláírás.

However, a predicate adjective can show plurality:

• Az aláírások fontosak. = The signatures are important.

So in your sentence, the adjectives inside the noun phrase stay unchanged, but the final predicate adjective could potentially appear as singular or plural depending on the construction and nuance.

In Hungarian, saját often refers to a possessor that is understood from context.

So saját kezű aláírás usually means:

• the person’s own handwritten signature
• their personally written signature

In legal or administrative language, the relevant person is often already obvious from the situation, so Hungarian does not always spell it out.

If you want to make the possessor explicit, you can say something like:

• az ügyfél saját kezű aláírása = the client’s own handwritten signature

So the original sentence leaves the owner implicit because the context is expected to make it clear.

Aláírás is the basic dictionary form: signature.

Aláírása means his/her/its signature or the signature of X, depending on context.

Your sentence uses the more general noun:

• a saját kezű aláírás = the handwritten/personal signature

If the sentence wanted to say explicitly his/her own signature, it could use a possessive form, for example:

• a saját kezű aláírása

But in formal Hungarian, the non-possessive version is often enough when the reference is already understood.