Chongqing, a city in Southwest China, is famous for its exciting nightlife.

1) nonessential information = a city [in Southwest China] (prep phrase)
2) Chongqing(subj) is(linking verb) famous (subj compl: adj) [3]
3) [for its exciting nightlife] (prep phrase)

But now, [something new is happening there].

Something new (subj)
is (linking verb)
happening (noun)
there. (adverb)

Young people are going to school at night to learn new things.

Young people(subj)
are (helping verb)
going (main verb)
[to school] // prep phrase
[at night] // prep phrase
[(to learn) new things]. // infinitive phrase

The special school(subj) is (linking verb) [in a park] (prep phrase).

It is not a normal school, but it is a place where you can learn.

It(subj) is(lv) not a (normal school) (subj compl: noun)
It(subj) is(lv) a place(subj compl: noun) [(where) you can learn] (subordinate clause).