يستعمل مصباحا رأسيا لكي يمشي في الليل.

Because the verb already includes the subject. يستعمل means he uses.

In Modern Standard Arabic, you often do not need to say هو unless you want extra emphasis or contrast. So:

• يستعمل مصباحًا... = He uses a lamp...
• هو يستعمل مصباحًا... = also He uses a lamp..., but with a more explicit subject

A verb-first order is very common and very natural in MSA. So يستعمل مصباحًا... is a normal neutral sentence pattern.

Arabic can also use subject-first order, but verb-first is extremely common in formal written Arabic.

Arabic usually shows indefiniteness by:

• not using الـ
• often using tanwīn in fully vocalized text

So مصباحًا means a lamp, not the lamp.

Compare:

• مصباحًا = a lamp
• المصباح = the lamp

Because it is the direct object of يستعمل, so it is in the accusative case.

In full spelling with vowel marks, it would be:

• مصباحًا

The ending -an is the indefinite accusative ending, and Arabic usually writes an extra alif with this ending. In unvowelled text, that often appears simply as مصباحا.

Because رأسيًّا is an adjective describing مصباحًا, and Arabic adjectives must agree with the nouns they describe.

So if مصباح is:

• masculine
• singular
• indefinite
• accusative

then the adjective must match:

• مصباحًا رأسيًّا

That is a very common Arabic pattern: noun first, then adjective.

It can mean either, depending on context.

The adjective رأسيّ can mean:

• of the head / head-mounted
• vertical

In this sentence, the intended meaning is most likely head-mounted, as in a headlamp, because of the context of walking at night.

لكي introduces a purpose. It means:

• so that
• in order to

So:

• لكي يمشي في الليل = so that he can walk at night
• or in order to walk at night

It explains why he uses the lamp.

Yes. After لكي, the following imperfect verb is normally in the subjunctive.

With full vowel marks, this would be:

• يَمْشِيَ

But in normal unvowelled Arabic writing, that often looks the same as يمشي, so learners may not see the difference in spelling.

So the grammar changes after لكي, even if the written form often looks unchanged.

Arabic often uses في with time expressions where English uses at.

So:

• في الليل literally = in the night
• natural English meaning = at night

This is just a normal difference between the two languages.

Arabic often uses the definite article with general time words and abstract time periods.

So في الليل is a normal way to mean at night in a general sense. English and Arabic do not always use articles in the same way.

Yes. In many contexts, يستعمل and يستخدم can both mean uses.

So both of these are possible:

• يستعمل مصباحًا رأسيًّا...
• يستخدم مصباحًا رأسيًّا...

Both are understandable and natural in MSA.