يناقش موظف الاستقبال تسجيل الوصول وتسجيل المغادرة.

Because Arabic very often uses verb–subject–object order, especially in formal written language.

So the structure here is:

• يناقش = the verb
• موظف الاستقبال = the subject
• تسجيل الوصول وتسجيل المغادرة = the objects

A very natural English-like order is subject–verb–object, and Arabic can do that too:

• موظف الاستقبال يناقش تسجيل الوصول وتسجيل المغادرة

Both are correct, but the original sentence uses a very common MSA pattern.

يناقش is the imperfect form of the verb ناقش.

In context, the imperfect can mean things like:

• discusses
• is discussing
• does discuss

The exact English tense depends on context.

It is 3rd person masculine singular, because the subject موظف الاستقبال is singular and masculine.

Because موظف الاستقبال is an iḍāfa construction, often called a possessive or noun-link construction.

Literally, it is something like:

• موظف = employee
• الاستقبال = the reception

Together: employee of the reception → naturally receptionist or front-desk employee

In an iḍāfa:

• the first noun usually does not take ال
• the second noun can make the whole phrase definite

So even without ال on موظف, the whole phrase is definite because of الاستقبال.

For the same reason: they are also iḍāfa phrases.

• تسجيل الوصول = registration of arrival
• تسجيل المغادرة = registration of departure

Idiomatic hotel English renders these as:

• check-in
• check-out

Again, in iḍāfa, the first noun normally does not take ال, so تسجيل stays without ال.

If you add the case endings, the sentence is:

يناقشُ موظفُ الاستقبالِ تسجيلَ الوصولِ وتسجيلَ المغادرةِ

Here is why:

• يناقشُ: the verb, ending in ـُ
• موظفُ: the subject, so it is nominative
• الاستقبالِ: second part of iḍāfa, so it is genitive
• تسجيلَ: direct object, so it is accusative
• الوصولِ: second part of iḍāfa, so it is genitive
• وتسجيلَ: another direct object, also accusative
• المغادرةِ: second part of iḍāfa, so it is genitive

In normal unvoweled Arabic writing, these endings are usually not shown.

Because ناقش is a directly transitive verb in MSA. It takes a direct object without a preposition.

So you say:

• يناقش الموضوع = he discusses the topic

not:

• يناقش عن الموضوع

This is similar to English discuss something, not discuss about something.

Yes, absolutely.

• يناقش موظف الاستقبال... = verb-first
• موظف الاستقبال يناقش... = subject-first

Both are grammatical.

The difference is mostly about style and emphasis:

• verb-first is very common in formal Arabic
• subject-first gives a little more prominence to the subject

In this sentence, both sound natural.

Because Arabic often keeps both fixed expressions complete:

• تسجيل الوصول
• تسجيل المغادرة

Repeating تسجيل makes the sentence clear and balanced.

You might sometimes see shorter coordination in other contexts, but here repeating the noun sounds neat and formal, especially because each phrase is a standard term.

No. It is a correct and formal expression, but it is not the only one.

You may also encounter:

• تسجيل الخروج

Both can be used for check-out, depending on context and style.

In this sentence, تسجيل الوصول and تسجيل المغادرة sound formal and fit a hotel or travel context well.

الاستقبال literally relates to reception or receiving.

In this phrase, it refers to the reception/front desk area, so:

• موظف الاستقبال = receptionist
• also possible in English: front-desk clerk / reception employee

So the phrase is not just any employee; it specifically means the person working at reception.