La misión empieza con un acertijo.

Because in Spanish, nouns often use an article where English might leave it out. La misión is the subject of the sentence, and using la makes it sound natural and complete.

Also, misión is a feminine noun, so it takes la in the singular:

• la misión
• una misión

This is one of the many cases where Spanish uses articles more regularly than English does.

Empieza is the conjugated form of the verb empezar.

The subject is la misión, which is third person singular (it), so the verb must match:

• empezar = to begin / to start
• empieza = begins / starts

So:

• La misión empieza = The mission begins / starts

Because empezar is a stem-changing verb. In the present tense, the e in the stem changes to ie in most forms.

Present tense of empezar:

• yo empiezo
• tú empiezas
• él / ella / usted empieza
• nosotros / nosotras empezamos
• vosotros / vosotras empezáis
• ellos / ellas / ustedes empiezan

So la misión empieza follows this normal stem-change pattern.

Yes. Comenzar and empezar both mean to begin / to start, and in this sentence they are both natural.

• La misión empieza con un acertijo
• La misión comienza con un acertijo

In everyday speech, empezar is often a little more common, but both are standard and correct.

Because Spanish uses empezar con to mean to start with.

So:

• empieza con = starts with
• La misión empieza con un acertijo = The mission starts with a riddle

This is a very common pattern:

• La película empieza con una escena oscura.
• La clase empieza con una pregunta.

Both can sometimes be translated as to start with, but they are not always used in exactly the same way.

• empezar con often means starting with something as the first element
• empezar por often means starting by / with something in a sequence, method, or choice of order

In this sentence, empieza con un acertijo sounds very natural because the mission opens with a riddle as its first part.

Examples:

• La reunión empieza con una presentación.
• Voy a empezar por lo más fácil.

So for this sentence, con is the most straightforward choice.

Yes. Acertijo is a masculine noun, so it takes un in the singular:

• un acertijo
• el acertijo

Even though the thing itself has no biological gender, Spanish nouns are grammatically masculine or feminine, and you have to learn the article with the noun.

Because un acertijo is not a person. The personal a is mainly used before a specific human direct object.

Examples:

• Veo a María.
• Busco a mi profesor.

But here, un acertijo is not a person, and after con you would not use the personal a anyway:

• con un acertijo is correct

The accent mark shows where the stress goes: mi-SIÓN.

Without the written accent, the word would not follow the normal spelling rules for stress. The accent mark tells you clearly that the last syllable is stressed.

In Spain Spanish pronunciation:

• misión ≈ mee-SYON
• more exactly: /miˈsjon/

The accent mark is important in writing and should not be left out.

In standard Spain Spanish, it is pronounced approximately:

a-ther-TI-ho

More exactly:

• a as in father
• ce often sounds like the without the final vowel in many parts of Spain: /θe/
• r is a light tap here
• ti is stressed: ti
• j is the strong Spanish sound /x/, like a throaty h

So the full pronunciation is roughly: /a.θer.ˈti.xo/

If you are learning Spain Spanish, that c before e and the j are both worth practicing.

Yes, but La misión empieza con un acertijo is the most neutral and natural order.

You might also hear:

• Empieza la misión con un acertijo

But that changes the emphasis slightly and is less neutral. For most learners, the standard pattern is best:

• subject + verb + rest

So the original sentence is the best version to learn first.

Spanish often uses the present tense for general statements, narration, summaries, or describing what happens in a story.

So La misión empieza con un acertijo can simply state what happens:

• in a game
• in a film plot
• in a story
• in a mission description

It does not have to mean that it is happening right now in a literal sense. Spanish, like English, often uses the present for this kind of description.