Die Firma möchte eine neue Regel einführen.

Because Firma is a feminine noun in German. German nouns have grammatical gender, and Firma takes the feminine article:

• die Firma = the company

This gender is grammatical, so it does not have to match anything logical in English. You simply learn Firma as a feminine noun.

Because Regel is also a feminine noun, and here it is in the accusative case as the direct object of the sentence.

The phrase breaks down like this:

• eine = a
• neue = new
• Regel = rule

Since Regel is feminine and singular, the indefinite article is eine in both nominative and accusative. The adjective neu also has to take an ending, so it becomes neue.

So:

• eine neue Regel = a new rule

möchte means would like to.

So:

• Die Firma möchte ... = The company would like to ...

It is the polite or softer form related to mögen. In everyday German, möchte is very common when talking about wishes or intentions.

Compare:

• Die Firma will eine neue Regel einführen. = The company wants to introduce a new rule.
  This sounds stronger and more direct.
• Die Firma möchte eine neue Regel einführen. = The company would like to introduce a new rule.
  This sounds softer.

Because möchte is a modal verb, and in German, when a modal verb is used with another verb, the second verb usually goes to the end of the clause in the infinitive.

Here:

• möchte = conjugated modal verb
• einführen = infinitive at the end

So the structure is:

• Subject + modal verb + other elements + infinitive

Example pattern:

• Die Firma möchte
  • eine neue Regel
    • einführen

This is very common in German:

• Ich möchte Deutsch lernen.
• Wir müssen jetzt gehen.
• Sie kann gut schwimmen.

Yes. einführen is a separable verb.

Its parts are:

• ein- = prefix
• führen = to lead / to carry / to introduce, depending on context

When it is used as a normal conjugated main verb, the prefix separates:

• Die Firma führt eine neue Regel ein.
  = The company introduces a new rule.

But when it stays in the infinitive, as it does after a modal verb, it stays together:

• Die Firma möchte eine neue Regel einführen.

So:

• führt ... ein = separated
• einführen = together in the infinitive

Because the main conjugated verb in this sentence is möchte, not einführt.

In German, only the finite (conjugated) verb takes the normal sentence position. Since möchte is the conjugated verb, einführen stays in the infinitive.

Compare:

• Die Firma führt eine neue Regel ein.
  No modal verb, so einführen is conjugated and separated.
• Die Firma möchte eine neue Regel einführen.
  With a modal verb, so einführen stays as an infinitive at the end.

Because after German modal verbs, you normally use the second verb in the bare infinitive, without zu.

So after verbs like:

• können
• müssen
• wollen
• sollen
• dürfen
• mögen / möchte

you do not use zu.

Correct:

• Die Firma möchte eine neue Regel einführen.

Not correct:

• Die Firma möchte zu einführen.

English learners often expect to introduce, but German does not use zu after a modal verb.

It is in the accusative case because it is the direct object of einführen.

Ask the question:

• What does the company want to introduce?

Answer:

• eine neue Regel

That makes it the direct object.

For feminine nouns, the indefinite article is:

• nominative: eine
• accusative: eine

So the article does not change here, but the phrase is still accusative because of its role in the sentence.

The basic structure is:

• Die Firma = subject
• möchte = finite verb
• eine neue Regel = object
• einführen = infinitive at the end

So the pattern is:

• Subject + finite verb + object + infinitive

German main clauses usually place the finite verb in the second position. That is exactly what happens here:

• Die Firma | möchte | eine neue Regel einführen

Yes. Das Unternehmen is another common way to say the company.

• die Firma = the company, often more everyday/business usage
• das Unternehmen = the company / enterprise, sometimes a bit more formal

So both are possible, depending on style and context.

Its main meaning is rule, but like many words, the exact translation depends on context.

Common uses include:

• eine Regel = a rule
• eine grammatische Regel = a grammar rule
• eine Vorschrift / betriebliche Regel = a regulation or company rule

In your sentence, eine neue Regel einführen most naturally means to introduce a new rule/policy.

Without möchte, you would conjugate einführen itself:

• Die Firma führt eine neue Regel ein.

This means:

• The company is introducing a new rule or
• The company introduces a new rule

Notice what changed:

• möchte ... einführen → modal verb + infinitive
• führt ... ein → conjugated separable verb

This is a very useful comparison for understanding German verb structure.