هو يتنفس بعمق.

Yes. In Arabic, يتنفس already tells you the subject is he because of the verb form.

So:

• هو يتنفس بعمق = He is breathing deeply
• يتنفس بعمق = also He is breathing deeply, if the context already makes the subject clear

Adding هو can:

• make the subject extra clear
• add emphasis
• help contrast with someone else, like هو يتنفس بعمق، وهي تتكلم = He is breathing deeply, and she is speaking

In ordinary Arabic, subject pronouns are often omitted unless needed.

يتنفس is in the imperfect verb form. In Modern Standard Arabic, the imperfect can express:

• a present action: he is breathing
• a habitual action: he breathes
• sometimes a near future meaning, depending on context

So by itself, هو يتنفس بعمق can mean either:

• He is breathing deeply
• He breathes deeply

The exact meaning depends on context.

The dictionary form is تَنَفَّسَ = to breathe.

So the forms are:

• تَنَفَّسَ = he breathed
• يَتَنَفَّسُ = he breathes / he is breathing

This verb is from Form V in Arabic morphology: تَفَعَّلَ / يَتَفَعَّلُ.

That pattern often gives a reflexive, internal, or process-like meaning. Here it is simply the normal verb for to breathe.

In the imperfect tense, Arabic uses prefixes to show the subject.

For تَنَفَّسَ:

• أتنفس = I breathe
• تتنفس = you breathe / she breathes
• يتنفس = he breathes
• نتنفس = we breathe

So يـ here marks the third person masculine singular: he.

Literally, بعمق means with depth or in depth.

It is made of:

• بـ = with / by / in
• عُمق = depth

Together, بعمق functions like the English adverb deeply.

So Arabic often uses a prepositional phrase where English uses an adverb:

• يتنفس بعمق = he breathes deeply

That is just a very natural Arabic way to express manner.

Arabic often says:

• بسرعة = quickly
  literally: with speed
• ببطء = slowly
  literally: with slowness
• بوضوح = clearly
  literally: with clarity
• بعمق = deeply
  literally: with depth

So even though English uses an -ly adverb, Arabic commonly prefers بـ + noun.

Yes, عُمق is a noun meaning depth.

Because it comes after the preposition بـ, it is grammatically in the genitive case.

In fully vowelled Arabic, you would see:

• بِعُمْقٍ

But in normal writing, short vowels and case endings are usually not written, so you normally just see:

• بعمق

A simple pronunciation guide is:

• huwa yatanffasu bi-ʿumq

More carefully:

• هُوَ = hu-wa
• يَتَنَفَّسُ = ya-ta-naf-fa-su
• بِعُمْقٍ = bi-ʿum-qin in full case pronunciation, though everyday careful MSA reading often sounds more like bi-ʿumq

A few important points:

• ع in عمق is a deep throat sound with no exact English equivalent
• فّ in يتنفس is doubled in the underlying pattern, so the middle part is pronounced with stress on that consonant
• the q in عمق is ق, a deeper k-like sound made farther back in the mouth

Yes, it is possible and natural.

This sentence has the order:

• هو = subject
• يتنفس = verb
• بعمق = adverbial phrase

So it is a subject–verb sentence.

Arabic also often uses verb–subject order, but with pronouns, starting with the pronoun is very common when the pronoun is stated explicitly.

So:

• هو يتنفس بعمق = perfectly normal
• يتنفس بعمق = also very normal
• يتنفس هو بعمق = possible, but usually more marked or emphatic

The verb changes to match the subject.

Examples:

• هي تتنفس بعمق = She is breathing deeply
• أنتَ تتنفس بعمق = You (masculine singular) are breathing deeply
• أنتِ تتنفسين بعمق = You (feminine singular) are breathing deeply
• نحن نتنفس بعمق = We are breathing deeply
• هم يتنفسون بعمق = They (masculine) are breathing deeply
• هن يتنفسن بعمق = They (feminine) are breathing deeply

This is a good example of how Arabic verbs agree with the subject.

In simple present-tense negation in MSA, use لا before the imperfect verb:

• هو لا يتنفس بعمق = He is not breathing deeply / He does not breathe deeply

So the pattern is:

• هو يتنفس بعمق = he breathes deeply
• هو لا يتنفس بعمق = he does not breathe deeply

In principle, Arabic sometimes uses an adverb-like accusative expression, but for this meaning the most natural standard phrasing is يتنفس بعمق.

So for a learner, the safest and most idiomatic expression is:

• يتنفس بعمق

It is best to learn this as a set phrase meaning to breathe deeply.

Yes, absolutely. It is a complete sentence with:

• a subject: هو
• a verb: يتنفس
• a phrase describing how the action happens: بعمق

So even without more context, it is a full, grammatical sentence in MSA.