A fényérzékenység nagy.

A is the Hungarian definite article, equivalent to the in English.

So:

• a fényérzékenység = the light sensitivity / the photosensitivity

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

Since fényérzékenység starts with a consonant sound, Hungarian uses a.

Here nagy is not directly modifying the noun inside a noun phrase. It is the predicate adjective of the sentence.

So the structure is:

• A fényérzékenység = the subject
• nagy = the predicate adjective, meaning is great/high/large

In English, we say:

• The photosensitivity is high

not:

• The high photosensitivity

Hungarian works the same way here. When the adjective is part of the predicate, it comes after the subject.

Yes — from an English point of view, there is an understood is.

In Hungarian, the verb van (to be) is usually left out in the third person singular present tense when the sentence is simply of the type X is Y.

So:

• A fényérzékenység nagy. = The photosensitivity is high.

But Hungarian does not normally say:

• A fényérzékenység van nagy. ✘

That would be ungrammatical in normal usage.

Fényérzékenység is a compound/derived noun. It can be broken down like this:

• fény = light
• érzékeny = sensitive
• -ség = a noun-forming suffix, often like -ness in English

So very literally, it is something like:

• light-sensitiveness
• more naturally: light sensitivity or photosensitivity

This kind of word formation is very common in Hungarian.

The suffix -ság / -ség turns adjectives into abstract nouns.

For example:

• boldog = happy → boldogság = happiness
• szép = beautiful → szépség = beauty
• érzékeny = sensitive → érzékenység = sensitivity

In fényérzékenység, the base idea is érzékenység (sensitivity), and fény- specifies what kind of sensitivity it is: sensitivity to light.

Yes. Nagy a fényérzékenység is also possible.

The difference is mainly about focus/emphasis.

• A fényérzékenység nagy. = neutral, straightforward statement
• Nagy a fényérzékenység. = puts more emphasis on nagy (it is high/great)

Hungarian word order is quite flexible, and changing it often changes what is emphasized rather than the core meaning.

That is a very natural question for English speakers.

Hungarian does not always match English adjective choices one-to-one. In many contexts where English uses high, Hungarian often uses nagy (big, great, large).

So for an abstract quantity, degree, or extent, nagy can be the natural choice.

Depending on context, Hungarian may also use magas in some cases, but nagy is very common for expressing that something is considerable, strong, or great in degree.

So here nagy does not necessarily mean physically big. It means something more like:

• great
• considerable
• high

No, it is not the same as the full sentence.

• A fényérzékenység nagy. = The photosensitivity is high.
• A nagy fényérzékenység = the high/great photosensitivity

The second one is only a noun phrase, not a complete sentence by itself.

So:

• nagy after the noun = part of the predicate
• nagy before the noun = directly modifies the noun

A rough guide is:

fayny-air-zay-keh-nyee-shayg

A few helpful points:

• é is a long vowel, somewhat like ay in say
• ny is like the ny in canyon
• sz is pronounced like English s
• s by itself is pronounced like English sh
• the final g is a hard g

Also, Hungarian stress normally falls on the first syllable:

• FÉNY-ér-zé-ke-nyiség

It is singular.

There is no special plural ending here. The Hungarian plural ending is usually -k, and that is not present.

So:

• fényérzékenység = sensitivity / photosensitivity
• fényérzékenységek = sensitivities

In this sentence, the subject is singular, and the predicate adjective nagy stays the same.

In the third person singular present tense, yes, typically:

• A fényérzékenység nagy. = The photosensitivity is high.
• A ház szép. = The house is beautiful.

But in other persons or tenses, the verb appears:

• Nagy vagyok. = I am big / great.
• Nagy volt. = It was big / great.
• Nagyok. = They are big.
  Here the plural predicate can appear without vannak in some styles, but learners usually first meet fuller patterns in contexts where the verb is overt in other structures.

The key beginner rule is: in simple present-tense he/she/it is sentences, Hungarian usually leaves out van.

Both are possible, depending on context.

• photosensitivity is often a good technical or medical translation
• light sensitivity is a more transparent everyday translation

Since you said the meaning is already shown to the learner, the main thing to notice is that the Hungarian word itself is quite literal in structure: light + sensitivity.

Yes, it is grammatical and natural, especially in technical, medical, or descriptive contexts.

Because fényérzékenység is a somewhat formal/technical word, the whole sentence sounds more like something from:

• a medical text
• a scientific description
• product specifications
• photography or materials science

But grammatically it is perfectly ordinary Hungarian.