Заявитель предъявит паспортные данные в случае если личные данные изменятся.

Заявитель means applicant, claimant, or the person submitting the application/request.

Although it is grammatically masculine singular, in official Russian it can refer to a person of any gender. So it works like English the applicant: the grammar is fixed, but the real person could be male or female.

Предъявит is the simple future of the perfective verb предъявить.

That is used because the sentence describes a single completed action in the future: the applicant will present the details if a certain condition is met.

• предъявляет = presents / is presenting (present tense, not right here)
• будет предъявлять = will be presenting or will present repeatedly/over a period of time, which does not fit this one-time action very well
• предъявит = will present once, as a completed act

In official Russian, this kind of future form is very common in instructions and regulations.

Предъявить usually means to present, to show for inspection, or to produce officially.

For example:

• предъявить паспорт = to show/present a passport
• предъявить удостоверение = to present an ID

In this sentence, it is being used with паспортные данные. That is understandable, but many native speakers would more naturally say:

• предоставить паспортные данные = provide passport details
• предъявить паспорт = present the passport itself

So the sentence is understandable, but slightly bureaucratic or not quite the most natural collocation.

They are related, but not the same.

• паспортные данные = passport details
  For example: passport number, series, issuing authority, date of issue

• личные данные = personal details / personal data
  For example: name, date of birth, surname, sometimes address or other identifying information

So the sentence means that the applicant will provide/pass on their passport details if their personal details change.

Because данные in this meaning is a plural-only noun in Russian.

Russian treats данные as plural:

• личные данные
• паспортные данные
• данные изменятся

So the verb must also be plural:

• данные изменятся = the data/details will change

This can feel strange to English speakers because English often uses data or information differently, but in Russian this word behaves grammatically as plural.

• паспортные данные is in the accusative plural, because it is the direct object of предъявит
• личные данные is in the nominative plural, because it is the subject of изменятся

Why do they look the same? Because for inanimate plural nouns, the accusative often has the same form as the nominative.

So:

• паспортные данные = accusative plural here
• личные данные = nominative plural here

В случае если is a more formal, official-sounding way to say if. It is close to English in the event that.

Compare:

• если личные данные изменятся = simple, neutral if the personal details change
• в случае если личные данные изменятся = more formal/legal/administrative

Since the sentence sounds bureaucratic, в случае если fits that style.

Very often, yes: many writers would write:

Заявитель предъявит паспортные данные в случае, если личные данные изменятся.

In formal writing, в случае, если is very common. You may also see в случае если without a comma when the whole phrase is treated as one conjunction.

For a learner, using в случае, если is usually the safest formal choice.

The -ся shows that the verb is being used intransitively: the data change themselves / undergo change.

• изменить что-то = to change something
• измениться = to change

So:

• личные данные изменятся = the personal details will change
• кто-то изменит личные данные = someone will change the personal details

This is a very common Russian verb pair:

• открыть / открыться
• изменить / измениться
• закрыть / закрыться

It is understandable and definitely sounds official, but many native speakers might choose a slightly different wording depending on the exact meaning.

If the person must show the physical passport:

• Заявитель предъявит паспорт, если личные данные изменятся.

If the person must provide passport details:

• Заявитель предоставит паспортные данные в случае, если личные данные изменятся.

So the original sentence is not wrong in the sense of being incomprehensible, but предъявить паспортные данные is a little less natural than either предъявить паспорт or предоставить паспортные данные.