التدريب التعريفي بدأ بالفعل.

Because Arabic allows both noun-first and verb-first word order.

Here, التدريب التعريفي بدأ بالفعل starts with the noun phrase, so it feels a bit like:

• As for the orientation training, it has already started.

Grammatically, التدريب التعريفي is the topic, and بدأ بالفعل is what is being said about it.

You could also say:

• بدأ التدريب التعريفي بالفعل

That version is also correct, but it is more verb-focused: The orientation training started already / has already started.

So the original sentence is natural; it just puts the training itself in the spotlight first.

Because التعريفي is an adjective describing التدريب, and in Arabic adjectives must match the nouns they describe in definiteness.

So:

• التدريب = the training
• التعريفي = the introductory / orientation-related

Together:

• التدريب التعريفي = the introductory training or the orientation training

Since the noun is definite with الـ, the adjective must also be definite with الـ.

Compare:

• تدريب تعريفي = an introductory training
• التدريب التعريفي = the introductory training

Here it is an adjective.

It comes after التدريب and describes what kind of training it is. That is a very common Arabic pattern:

• noun + adjective

So:

• التدريب = training
• التعريفي = introductory / orientation-related

Because it follows the noun and agrees with it, it works as an adjective.

It is related to the noun تعريف, which can mean introduction, identification, or definition, depending on context.

The ending ـي often forms a descriptive adjective, sometimes called a nisba adjective. So تعريفي means something like:

• introductory
• for introduction
• orientation-related

In this sentence, التدريب التعريفي is best understood as orientation training or introductory training.

Because Arabic often uses the simple past where English uses either:

• started
• has started
• has already started

The word بدأ is the past tense: began / started.

When Arabic adds بالفعل, it often gives the sense of already or indeed, so the whole sentence naturally conveys:

• has already started

So this is a normal Arabic way to express a completed action that is relevant now.

In this sentence, بالفعل means already.

Its broader meanings can include:

• actually
• indeed
• in fact
• really
• already

The exact meaning depends on context.

Here, with بدأ, it most naturally means:

• has already started

So بدأ بالفعل = already started / has indeed started

No. Arabic does not need an extra pronoun here.

The subject is already clear from التدريب التعريفي, so adding هو would usually be unnecessary.

Arabic often says simply:

• التدريب التعريفي بدأ بالفعل

not:

• التدريب التعريفي هو بدأ بالفعل

That second version would sound unnatural in normal MSA.

A fully vocalized version would be:

• التَّدْرِيبُ التَّعْرِيفِيُّ بَدَأَ بِالْفِعْلِ

A few notes:

• التدريبُ is nominative because it is the topic/subject.
• التعريفيُّ matches it and is also nominative.
• بدأَ is a past-tense verb.
• بالفعلِ ends with kasra because it comes after the preposition بـ.

In normal everyday writing, these short vowels are usually omitted.

بدأ is pronounced approximately bada’a.

The hamza ء represents a glottal stop, a brief catch in the throat. So it is not just badaa. There is a small break:

• ba-da-ʾa

This verb is a common one meaning to begin or to start.

Its root is ب د أ.

In both words, the ل of الـ is not pronounced normally, because the next letter is ت, which is a sun letter.

So:

• التدريب is pronounced at-tadrīb
• التعريفي is pronounced at-taʿrīfiyy

This is why, in full vocalization, you see a shadda on the ت:

• التَّدْرِيب
• التَّعْرِيفِيّ

So although it is written ال, it is pronounced more like at- here.

Yes, that is also correct.

The difference is mainly one of focus and style:

• التدريب التعريفي بدأ بالفعل
  More topic-first; it highlights the orientation training.

• بدأ التدريب التعريفي بالفعل
  More action-first; it highlights the fact that it started.

Both are natural in MSA, and the meaning is very close.

Because Arabic does not need a helping verb here.

English often uses forms like:

• has started
• has already started

Arabic can express that same idea with just:

• a past-tense verb: بدأ
• plus an adverb/expression like بالفعل

So بدأ بالفعل is complete by itself and does not need an extra verb such as كان.