Для короткометражки нужна съёмочная группа.

Because нужна agrees with съёмочная группа, which is a feminine singular noun phrase.

• группа = group, and it is feminine
• so the short-form adjective нужен / нужна / нужно / нужны must match it

Compare:

• нужен актёр = an actor is needed
• нужна группа = a group is needed
• нужно оборудование = equipment is needed
• нужны люди = people are needed

So in this sentence:

• съёмочная группа = feminine singular
• therefore: нужна съёмочная группа

Because it comes after для, and для requires the genitive case.

The base form is:

• короткометражка = short film

After для:

• для короткометражки = for the short film / for a short film

This is a very common pattern:

• для фильма = for the film
• для проекта = for the project
• для работы = for work

So короткометражки is the genitive singular form of короткометражка.

Yes, it is a normal and very common word in everyday Russian. It means short film or short movie.

It comes from короткометражный фильм, which is more formal/literal:

• короткометражный = short-length
• фильм = film

So:

• короткометражный фильм = short film
• короткометражка = short film, in a shorter and more conversational form

A native speaker would use короткометражка very naturally.

A fairly literal breakdown is:

• Для короткометражки = for the short film
• нужна = is needed
• съёмочная группа = a film crew

So literally:

• For the short film, a film crew is needed.

This is a very natural Russian structure. English often says:

• The short film needs a film crew or
• A film crew is needed for the short film

Russian often expresses this idea with нужен / нужна / нужно / нужны.

That version is possible in principle, but it sounds more formal and less natural for this kind of everyday statement.

Russian usually prefers the simpler pattern:

• Для короткометражки нужна съёмочная группа.
• Короткометражке нужна съёмочная группа.

Both mean roughly The short film needs a film crew / A film crew is needed for the short film.

The verb нуждаться в means to be in need of, but it is more formal/bookish:

• Проект нуждается в финансировании. = The project needs funding.

For ordinary conversation, нужен / нужна / нужно / нужны is often the most natural choice.

Yes. A very common alternative is:

• Короткометражке нужна съёмочная группа.

Here, короткометражке is in the dative case, and the meaning is:

• The short film needs a film crew.

So you have two useful patterns:

• Для короткометражки нужна съёмочная группа. = A film crew is needed for the short film.
• Короткометражке нужна съёмочная группа. = The short film needs a film crew.

They are very close in meaning. The version with для focuses a bit more on for the purposes of the short film.

Word for word:

• съёмочная = filming / production-related
• группа = group

Together, съёмочная группа is the standard expression for film crew or production crew.

It is a set phrase. Even though the literal parts are filming group, the normal English translation is film crew.

The hard sign ъ separates the prefix-like part from the following iotated vowel.

In съёмочная:

• съ-
  • ём...

Its job is not to add its own sound, but to prevent the sounds from blending too much and to signal that ё keeps its y-like onset.

Very roughly, съё sounds like syo with a clear separation.

Also remember:

• ё is always stressed when written
• so the stress in съёмочная is on ё

A helpful approximation is:

• syomachnaya groopa

More carefully:

• съёмочная → stress on ё
• группа → stress on the first syllable: гру́ппа

So:

• съё́мочная гру́ппа

A couple of useful notes:

• ё = yo
• чн in съёмочная is pronounced like chn
• группа has a doubled пп in spelling, though in normal speech you do not need to exaggerate it much

Yes. Russian word order is flexible, and different orders can change the emphasis.

The original:

• Для короткометражки нужна съёмочная группа.

Other possible versions:

• Съёмочная группа нужна для короткометражки.
• Нужна съёмочная группа для короткометражки.

All are understandable and natural in the right context.

Very roughly:

• Для короткометражки... puts the for the short film part first
• Съёмочная группа нужна... highlights the film crew
• Нужна съёмочная группа... can sound like introducing new information: What is needed? A film crew.

Because съёмочная группа is simply a singular noun phrase in Russian, just like group is singular in English.

Even though it refers to multiple people, grammatically it is one unit:

• эта группа = this group
• группа нужна = the group is needed

Russian treats many collective nouns this way. The meaning may involve several people, but the grammar is singular.

No. Russian has no articles.

So съёмочная группа can mean:

• a film crew
• the film crew

The exact meaning depends on context.

In this sentence, without extra context, English will usually translate it as:

• A film crew is needed for the short film.

because it sounds like new, indefinite information.

It is mostly neutral and natural.

• нужна is completely standard
• съёмочная группа is standard
• короткометражка is slightly less formal than короткометражный фильм, but still very normal

So the whole sentence sounds like everyday standard Russian, especially in a filmmaking or project context.