Learn Hardcore Polish: Inni uczniowie lubią ten film.

It’s the nominative plural masculine personal form of inny (other).
It matches uczniowie (students/pupils), which is also masculine personal plural nominative.

So inni uczniowie = other students (other than some previously mentioned group).

Why is it inni uczniowie, not inne uczniowie or inne dzieci?

In Polish, adjectives (and adjective-like words such as inny) must agree with the noun in gender, number and case.

uczniowie = masculine personal, plural, nominative
→ needs inni (masculine personal plural).
dzieci = technically neuter plural (but behaves irregularly)
→ would take inne dzieci (not inni).

Examples:

inni uczniowie – other (male / mixed group of) pupils
inne uczennice – other (female) pupils
inne dzieci – other children

Why is it uczniowie and not the dictionary form uczeń?

Uczeń is the singular form: a pupil / a student (school-age).

Here we are talking about more than one student, so we need the plural:

1 – uczeń
2, 3, 4 – uczniowie (in Nominative: dwaj / trzej uczniowie)
5+ – grammar gets trickier in real sentences, but the nominative plural is still uczniowie.

The sentence Inni uczniowie lubią ten film is about other students (plural), so uczniowie is required.

Could we say Inni studenci lubią ten film instead of inni uczniowie?

Yes, but the meaning changes slightly:

uczniowie = usually school pupils (primary, middle, sometimes high school)
studenci = university/college students

Grammatically, both work:

Inni uczniowie lubią ten film. – Other pupils like this film.
Inni studenci lubią ten film. – Other (university) students like this film.

The form inni is still correct in both, because both uczniowie and studenci are masculine personal plural.

Why is it lubią, not lubiący or lubiące?

Lubią is the finite verb form: 3rd person plural, present tense of lubić (to like).

lubię – I like
lubisz – you (sg.) like
lubi – he/she/it likes
lubimy – we like
lubicie – you (pl.) like
lubią – they like

Since inni uczniowie = they, the verb must be lubią.

Forms like lubiący/lubiące are participles (liking) and would be used differently, e.g. uczniowie lubiący ten film (students liking this film).

Why is it ten film, not ta film or to film?

The noun film in Polish is:

masculine, inanimate, singular.

The basic demonstrative pronoun this must agree with it:

ten – masculine (e.g. ten film, ten samochód)
ta – feminine (e.g. ta książka, ta szkoła)
to – neuter (e.g. to dziecko, to okno)

So ten film is correct: this film / that film (context decides how it’s translated).

Is ten film in the nominative or accusative case here?

Formally, ten film here is accusative singular masculine inanimate, because it’s the direct object of lubią.

For masculine inanimate nouns, nominative and accusative look the same:

Nominative: ten film jest ciekawy – this film is interesting.
Accusative: inni uczniowie lubią ten film – other students like this film.

So the form doesn’t change, but the function in the sentence is accusative.

Can we change the word order, like Ten film lubią inni uczniowie?

Yes. Polish word order is fairly flexible. Different orders change the emphasis, not the core meaning.

Inni uczniowie lubią ten film.
Neutral-ish: states that other students like this film.
Ten film lubią inni uczniowie.
Emphasises this film first, then who likes it. Could feel like: “This film is liked by other students.”
Lubią ten film inni uczniowie.
Focus on the verb and maybe contrast:
“(Yes,) other students like this film.”

All are grammatically correct; the “most neutral” is usually subject–verb–object:
Inni uczniowie lubią ten film.

What’s the difference between inni uczniowie and pozostali uczniowie?

Both can be translated as other students, but the nuance differs:

inni uczniowie – simply other students (not the ones we just referred to). Fairly neutral.
pozostali uczniowie – the remaining students / the rest of the students, i.e. all others not in the first group.

Example contrast:

Jan i Piotr nie lubią tego filmu. Inni uczniowie lubią ten film.
Jan and Piotr don’t like this film. Other students do.
(Could be some of them, could be most of them.)
Jan i Piotr nie lubią tego filmu. Pozostali uczniowie lubią ten film.
Jan and Piotr don’t like this film. The rest of the students like it.
(Strong suggestion: everyone except Jan and Piotr likes it.)

Does lubią here mean “are liking” or “like” in general?

Polish doesn’t have a separate present continuous form like English.

Lubią can mean:

(generally) like – their usual opinion:
Inni uczniowie lubią ten film. – Other students like this film (in general).
In context, you virtually never translate lubią as are liking. It’s understood as a general preference.