Компания решила уволить директора.

Because компания is a feminine noun in Russian. In the past tense, Russian verbs agree with the subject in gender and number:

• он решил = he decided
• она решила = she decided
• оно решило = it decided
• они решили = they decided

So Компания решила literally means The company decided, with the verb matching the feminine noun компания.

Because after решить (to decide), Russian often uses an infinitive, just like English:

• решила уволить = decided to fire / decided to dismiss

So the structure is:

• Компания = the company
• решила = decided
• уволить = to fire
• директора = the director

This is a very common pattern in Russian: решить + infinitive.

Because директора is the accusative case here: the director is the direct object of уволить.

With animate masculine nouns, the accusative singular usually looks like the genitive singular:

• nominative: директор
• genitive: директора
• accusative (animate): директора

Since a director is a person, Russian treats him as animate, so you get уволить директора.

Good question, because директора can also be a plural form in some contexts.

Here it is singular because:

1. The meaning is to fire the director, not the directors.
2. After уволить, a single animate masculine noun often appears in accusative singular, which matches the genitive singular form.
3. If it were plural, the rest of the sentence would usually make that clearer from context.

So in this sentence, директора = the director (singular).

Because уволить is the perfective form, while увольнять is the imperfective form.

• уволить = to fire/dismiss someone as a completed action
• увольнять = to be firing / to fire in general / repeatedly / as a process

After решить, Russian often prefers the perfective infinitive when talking about a specific intended result:

• Компания решила уволить директора.
  = The company decided to fire the director.

This focuses on the single completed action they decided to take.

It most often means to dismiss, to fire, or to terminate someone’s employment. In English, the best translation depends on context.

• If someone is removed from their job for performance or discipline, fire fits well.
• In more neutral or formal contexts, dismiss or terminate may be better.
• Lay off usually suggests staff cuts or economic reasons, and уволить does not automatically imply that.

So уволить директора most naturally means to fire/dismiss the director.

Yes. Russian word order is more flexible than English because case endings show grammatical roles.

The neutral order here is:

• Компания решила уволить директора.

But you could also hear:

• Директора решила уволить компания.
• Уволить директора решила компания.

These alternatives may change emphasis or sound more literary, dramatic, or contrastive. For a learner, the original version is the most neutral and safest.

Russian has no articles like a or the.

So:

• компания can mean a company or the company
• директора can mean a director or the director

You figure out whether it is definite or indefinite from context. In many example sentences, English uses the because that sounds most natural in translation, but Russian does not mark this directly.

Yes. In Russian, grammatical gender is a property of the noun, not necessarily of real-world biological sex.

• компания ends in -я, so it is a feminine noun.
• That is why the past-tense verb is решила.

This is the same idea as with many non-human nouns in Russian: they still have grammatical gender and control agreement.

Here are the dictionary forms:

• компания = company
• решить = to decide
• уволить = to fire / dismiss
• директор = director

In the sentence, решила is the past tense form of решить, and директора is the accusative singular form of директор.

The stress is:

• компАния
• решилА
• уволИть
• дирЕктора or often директорА depending on usage and speaker, but in standard modern Russian дирЕктор is nominative and дирЕктора is the usual singular oblique form

A practical learner-friendly pronunciation is:

• компАния решилА уволИть дирЕктора

If you are learning to say it naturally, the biggest thing to remember is that решила has stress on the last -а.

No. It means the company decided to remove the director from his job.

If the director quit voluntarily, Russian would use a different verb, such as:

• директор решил уволиться = the director decided to resign / quit

Compare:

• уволить директора = to fire the director
• уволиться = to resign / quit oneself

That -ся makes a big difference.