Он притворяется спокойным.

Because притворяться is the verb that means to pretend / to feign / to act as if one is.

So:

• Он спокойный = He is calm / He’s a calm person
• Он спокоен = He is calm (state)
• Он притворяется спокойным = He is pretending to be calm

The sentence is not simply describing his state. It says he is acting calm, whether or not he really feels that way.

Притворяется is:

• 3rd person singular
• present tense
• from the verb притворяться

That matches он = he.

A quick conjugation of притворяться in the present:

• я притворяюсь = I pretend
• ты притворяешься = you pretend
• он / она притворяется = he / she pretends
• мы притворяемся = we pretend
• вы притворяетесь = you pretend
• они притворяются = they pretend

The -ся is part of the verb притворяться. Many Russian verbs have this reflexive ending.

Here, it does not literally mean he is pretending himself in the natural English sense. It is simply the normal dictionary form of the verb:

• притворяться = to pretend, to feign

So you should learn притворяться as a whole verb.

Because after притворяться, the word describing what someone is pretending to be usually goes into the instrumental case.

So:

• спокойный = nominative masculine singular
• спокойным = instrumental masculine singular

Russian says, in effect, He pretends to be calm, and the complement after притворяться takes instrumental.

More examples:

• Он притворяется больным. = He is pretending to be sick.
• Она притворяется доброй. = She is pretending to be kind.
• Они притворяются уставшими. = They are pretending to be tired.

Because спокойным is masculine singular instrumental, which matches он.

If the subject changed, the adjective would change too:

• Он притворяется спокойным.
• Она притворяется спокойной.
• Оно притворяется спокойным.
• Они притворяются спокойными.

So the adjective agrees with the person or thing doing the pretending.

No. The meanings are quite different.

• Он спокоен = He is calm.
• Он притворяется спокойным = He is pretending to be calm.

The second sentence suggests that he may actually be worried, upset, afraid, or nervous, but he is trying to appear calm.

Yes.

• притворяться = imperfective
• притвориться = perfective

In your sentence, притворяется is imperfective, which fits an ongoing or repeated action in the present.

Compare:

• Он притворяется спокойным. = He is pretending to be calm. / He pretends to be calm.
• Он притворился спокойным. = He pretended to be calm. / He made himself seem calm for that moment.

Very roughly:

• imperfective = process, ongoing behavior, repeated action
• perfective = completed act or single result

Yes, sometimes.

Russian often drops subject pronouns when the context makes the subject clear. So in the right context, you could say simply:

• Притворяется спокойным.

This would mean He is pretending to be calm or She is pretending to be calm, depending on context.

But with no context, он helps make it clear that the subject is he.

Yes. Russian word order is flexible, though the neutral order here is:

• Он притворяется спокойным.

Other orders are possible for emphasis, for example:

• Спокойным он притворяется.
• Он спокойным притворяется.

These are not random; they can shift emphasis or sound more marked. For learners, the original order is the safest and most natural default.

This is an important meaning difference:

• притворяться = to pretend, deliberately give a false impression
• казаться = to seem, to appear

So:

• Он притворяется спокойным. = He is intentionally acting calm.
• Он кажется спокойным. = He seems calm.
  (This does not necessarily mean he is faking it.)

So притворяться usually implies conscious deception or acting.

A simple pronunciation guide:

• Он = on
• притворяется ≈ preet-va-RYA-yet-sa
• спокойным ≈ spa-KOY-nym

Stress:

• притворя́ется
• споко́йным

So the whole sentence is roughly:

on preet-va-RYA-yet-sa spa-KOY-nym

This is only an approximation, but it can help you recognize the spoken form.