На вокзале молодая пара целовалась и долго не хотела прощаться.

Because на вокзале answers the question where? and uses the prepositional case after на.

• на вокзале = at the station
• на вокзал would mean to the station and uses the accusative case, answering where to?

So here:

• На вокзале = At the station

In Russian, пара is grammatically a singular noun, even though it refers to two people as a unit.

So the verbs agree with пара, not with the two individuals inside it:

• молодая пара
• пара целовалась
• пара не хотела

This is similar to English the couple was... in styles where couple is treated as singular.

Because the adjective must agree with the noun it describes in gender, number, and case.

• пара is feminine singular
• so the adjective must also be feminine singular
• therefore: молодая пара

Compare:

• молодой человек = young man
• молодая женщина = young woman
• молодая пара = young couple

Again, the verb agrees with пара, which is singular feminine.

Past-tense Russian verbs show gender and number:

• целовался = masculine singular
• целовалась = feminine singular
• целовалось = neuter singular
• целовались = plural

Since пара is feminine singular, the correct form is целовалась.

The ending -ся (or -сь) often makes a verb reflexive, but in many cases it has a broader meaning than simple oneself.

Here целоваться means to kiss each other / to be kissing.

So:

• целовать = to kiss someone
• целоваться = to kiss each other / to be kissing

In this sentence, целовалась means the couple were engaged in kissing each other, not that one person kissed themself.

Because the subject is still пара, which is grammatically singular feminine.

So:

• пара хотела = the couple wanted
• пара не хотела = the couple did not want

Even though the meaning involves two people, the grammar follows the noun пара.

Прощаться means to say goodbye or to part, often with the sense of a mutual farewell.

The non-reflexive прощать usually means something completely different: to forgive.

So these are different verbs:

• прощать = to forgive
• прощаться = to say goodbye / to part

That is why the reflexive form is necessary here.

Both are possible in some contexts, but they give slightly different shades of meaning.

• прощаться = imperfective, focusing on the process or situation of saying goodbye
• попрощаться = perfective, focusing on the completed act of saying goodbye

In this sentence, не хотела прощаться sounds natural because it emphasizes their reluctance to begin or go through the farewell.

It has the feeling of:

• they kept delaying the goodbye
• they did not want to part

If you said не хотела попрощаться, it would sound more like did not want to say goodbye (as a completed act).

Долго means for a long time or a long time.

It modifies the second part of the sentence:

• долго не хотела прощаться = did not want to say goodbye for a long time

In natural English, this is often expressed as:

• didn’t want to say goodbye for a long time
• were reluctant to say goodbye for a long time
• took a long time saying goodbye

Russian has no articles like English a/an/the.

So молодая пара can mean:

• a young couple
• the young couple

Which one is meant depends on context. In an isolated sentence like this, English usually chooses a young couple unless the couple has already been mentioned.

The word order is fairly natural, but Russian word order is more flexible than English.

This sentence is:

• На вокзале молодая пара целовалась и долго не хотела прощаться.

A different order is also possible, for example:

• Молодая пара на вокзале целовалась и долго не хотела прощаться.

Both mean basically the same thing. The original version begins with На вокзале to set the scene first: At the station...

That is very common in Russian.

Normally, no. In this context it means to say goodbye / to part, not to end the relationship.

Because the sentence mentions:

• На вокзале = at the station
• целовалась = they were kissing

the most natural meaning is that they were seeing each other off and did not want to separate at that moment.

So this is about a farewell scene, not a romantic breakup.