Она попрощалась и ушла.

Because the subject is она (she), and both verbs are in the past tense, feminine singular.

In Russian past tense, the verb agrees with gender and number:

• он ушёл = he left
• она ушла = she left
• оно ушло = it left
• они ушли = they left

The same thing happens with попрощалась:

• он попрощался
• она попрощалась

So -ла is the normal feminine singular past ending.

The dictionary form is попрощаться, which is a reflexive verb. Reflexive verbs in Russian end in -ся or -сь.

So:

• попрощаться = to say goodbye
• попрощалась = she said goodbye

The ending -сь here is just the reflexive marker in a form where it sounds natural after a vowel. You will often see -ся / -сь alternate depending on the form.

This -ся / -сь does not always mean a truly reflexive action like wash oneself. In many verbs, it is simply part of the verb itself. Попрощаться is one of those.

The dictionary forms are:

• попрощаться = to say goodbye
• уйти = to leave, go away

This is important because Russian dictionaries usually list verbs in the infinitive, not in the past tense form you see in the sentence.

A learner might not immediately recognize ушла as coming from уйти, because the stem changes:

• уйти
• ушёл / ушла / ушли

That is normal for this verb.

Because ушла means left / went away, while пошла usually means set off / started going.

Compare:

• Она ушла. = She left.
• Она пошла домой. = She started going home / she went home.

In Она попрощалась и ушла, the idea is that she said goodbye and then departed. So ушла is the natural choice.

Both verbs are perfective:

• попрощаться — perfective
• уйти — perfective

Perfective verbs present actions as completed whole events. That fits this sentence well, because it describes two finished actions in sequence:

1. she said goodbye
2. she left

If you used imperfective verbs instead, the meaning would change. For example:

• Она прощалась и уходила.

This could sound like background narration, repeated behavior, or a less sharply completed sequence, depending on context. The original sentence is much cleaner and more natural for a single completed event.

Because this is a simple sentence with one subject and two coordinated verbs:

• Она = subject
• попрощалась and ушла = two actions of the same subject

In Russian, just as in English, you normally do not put a comma before и when it simply connects two parts like this:

• Она попрощалась и ушла.

A comma would usually appear only in more complicated structures.

Yes, very often.

Russian frequently leaves out subject pronouns when the subject is clear from context. So in a story or conversation, you could easily say:

• Попрощалась и ушла.

This still means She said goodbye and left, if the listener already knows who is being talked about.

Including она can make the sentence:

• clearer,
• slightly more explicit,
• or sometimes a bit more contrastive, depending on context.

It is very close to said goodbye, but it is a single verb in Russian, not a phrase.

So:

• попрощаться = to say goodbye / to take leave

It is often more natural than translating word-for-word from English. Russian could also express the idea with a phrase such as сказала до свидания, but попрощалась is compact and very idiomatic.

Because Russian, like English, commonly uses one subject for a sequence of actions:

• Она попрощалась и ушла.
• She said goodbye and left.

There is no need to repeat она before ушла, because it is already understood that the same person did both actions.

If Russian repeated the subject, it would usually sound unnecessary unless there were a special reason for emphasis.

The main difference is aspect.

• попрощалась = perfective, a completed act of saying goodbye
• прощалась = imperfective, saying goodbye / was saying goodbye / used to say goodbye

Examples:

• Она попрощалась и ушла. = She said goodbye and left.
  This is a single finished event.

• Она долго прощалась. = She was saying goodbye for a long time.
  This focuses on the process.

So in your sentence, попрощалась is used because the action is presented as complete.

This is one of those Russian verbs that changes stem.

The infinitive is:

• уйти

But the past tense forms are:

• ушёл = he left
• ушла = she left
• ушло = it left
• ушли = they left

So you just have to learn this as the normal past-tense pattern of уйти. Many common Russian motion verbs are somewhat irregular, so this is a good one to memorize early.

Yes, Russian word order is flexible, but the neutral order here is very natural:

• Она попрощалась и ушла.

If you change the order, the emphasis changes. For example:

• Попрощалась она и ушла.
  This sounds marked or stylistic.

• Ушла, попрощавшись.
  This is a different structure: She left after saying goodbye.

So while Russian allows variation, the original version is the most straightforward and neutral way to say it.

Only the past-tense verb forms would change.

Masculine:

• Он попрощался и ушёл. = He said goodbye and left.

Plural:

• Они попрощались и ушли. = They said goodbye and left.

This is a good example of how Russian past tense agrees with the subject in gender and number.