Az új szabály ellen vagyok.

Hungarian uses a / az for the, and the choice depends on the following sound.

• a before a consonant sound
• az before a vowel sound

Here, the next word is új, which begins with a vowel sound, so it must be:

• az új szabály = the new rule

Even though szabály starts with sz-, the article matches the word that immediately follows it, which is új.

Ellen means against.

In Hungarian, ellen is a postposition, which means it comes after the noun phrase, not before it like English against.

So:

• az új szabály ellen = against the new rule

Compare the word order:

• English: against the new rule
• Hungarian: the new rule against

That is completely normal in Hungarian.

Because ellen takes the noun in its basic form, not in the accusative.

So you say:

• a szabály ellen = against the rule

not:

• a szabályt ellen ✗

This is a common thing to learn with Hungarian postpositions: many of them use the noun without an extra case ending.

Vagyok means I am.

It is the first person singular form of the verb van (to be).

Some useful forms are:

• vagyok = I am
• vagy = you are
• van = he/she/it is

So:

• Az új szabály ellen vagyok. = I am against the new rule.

Hungarian usually leaves out subject pronouns when they are already clear from the verb ending.

Since vagyok already means I am, you do not need én.

So both are possible:

• Az új szabály ellen vagyok. = neutral, natural
• Én az új szabály ellen vagyok. = I am against the new rule (extra emphasis or contrast)

Hungarian does this a lot, so omitted pronouns are very common.

Not completely. Hungarian word order is flexible, and changing it often changes the focus or emphasis.

A neutral sentence is:

• Az új szabály ellen vagyok.

You could also say:

• Én az új szabály ellen vagyok.
  This puts more emphasis on I.

In many contexts, the basic sentence sounds natural and straightforward. Hungarian word order often depends more on what you want to highlight than on rigid grammatical rules.

Yes, in many situations that is a natural English translation.

Literally, it is:

• I am against the new rule

But in normal English, that often overlaps with:

• I oppose the new rule

The Hungarian sentence expresses a position or opinion. It does not necessarily sound highly formal or dramatic; it simply means the speaker is not in favor of the rule.

No, not in this structure.

Because ellen is a postposition, it normally comes after the noun phrase:

• az új szabály ellen ✓

not:

• ellen az új szabály ✗

So if you want to say against the new rule, the natural Hungarian structure is noun phrase + ellen.

Because új is an adjective meaning new, and here it simply modifies szabály (rule).

Hungarian adjectives do not have to agree in number or gender the way they do in many European languages. In this sentence:

• új = new
• szabály = rule

So:

• az új szabály = the new rule

There is no gender marking, and the adjective stays in its basic form here.

Yes, very common.

The pattern is:

• [something] ellen vagyok = I am against [something]

Examples:

• A terv ellen vagyok. = I am against the plan.
• Az ötlet ellen vagyok. = I am against the idea.

A related form is to use a pronoun:

• Ellene vagyok. = I am against it / him / her.

So this sentence uses a very useful everyday pattern.