يحزم معطفا واقيا من المطر لكي يمشي في المطر.

Because the verb يحزم already tells you the subject.

In MSA, a finite verb usually includes:

• person
• number
• gender

So يحزم means he packs or he is packing.
You only need هو if you want extra emphasis or contrast.

يحزم comes from the root ح-ز-م and commonly means to pack, to bundle, or to prepare/pack up.

In this sentence, the most natural meaning is something like:

• he packs
• he packs along
• he gets ready with

The exact English wording depends on the translation you were given, but the core idea is that he is preparing the coat for use.

معطفًا is the direct object of يحزم.

So:

• يحزم = he packs
• معطفًا = a coat

Because it is:

• indefinite = a coat, not the coat
• accusative = direct object of the verb

it takes the accusative indefinite ending -ًا in full vocalization: معطفًا.

Because Arabic adjectives normally come after the noun they describe.

So:

• معطفًا = a coat
• واقيًا = protective

Together:

• معطفًا واقيًا = a protective coat

The adjective must agree with the noun in:

• definiteness
• gender
• number
• case

Here both are:

• masculine
• singular
• indefinite
• accusative

This is a very good question, because واقيًا is a form that often confuses learners.

The basic adjective is واقٍ, meaning protective or shielding.

When this kind of word is indefinite accusative, it becomes واقيًا.

So you can think of it like this:

• nominative/genitive indefinite: واقٍ
• accusative indefinite: واقيًا

That is why you see the longer form here: it matches معطفًا, which is also accusative.

Here من is best understood as from in the sense of against or protecting from.

So:

• واقيًا من المطر = protective from the rain
• more natural English: rainproof or protective against rain

It does not mean the coat comes from the rain as a source.
It describes what the coat protects you against.

Yes. It is a clear, descriptive MSA expression.

Literally, it means:

• a coat protective against rain

That works well in formal Arabic. Arabic often uses descriptive phrases like this rather than a single compact noun.

In fully inflected form inside this sentence, it appears as:

• معطفًا واقيًا من المطر

لكي means so that, in order that, or in order to.

It introduces a purpose clause.

So:

• لكي يمشي في المطر = so that he can walk in the rain / in order to walk in the rain

It tells you why he is packing the raincoat.

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

So the fully vocalized form is:

• لِكَيْ يَمْشِيَ

However, in normal unvocalized writing, يمشي often looks the same whether you are thinking of it as indicative or subjunctive. The grammatical change is clearer when full vowel marks are written.

So in this sentence:

• لكي triggers the subjunctive
• يمشي means he may walk / he can walk / he walk, depending on how you translate the purpose in English

Arabic often uses the definite article with weather and general natural phenomena, where English may or may not use the.

So:

• من المطر
• في المطر

both naturally use المطر = the rain

In English, we often just say rain in a general sense, but Arabic commonly says the rain in these contexts.

Also, after من and في, المطر is grammatically genitive:

• مِنَ الْمَطَرِ
• فِي الْمَطَرِ

The case ending is usually not written in ordinary text.

Because في is the normal preposition here.

So:

• يمشي في المطر = he walks in the rain

This is very similar to English.
Arabic is not saying he is physically inside rain as a container; it is just the normal idiomatic way to express being out in rainy conditions.

Yes, that repetition is completely normal.

The sentence says:

• the coat protects from rain
• the purpose is to walk in the rain

Even though English sometimes tries to avoid repetition more strongly, Arabic often repeats a noun when it keeps the meaning clear and direct.

So the repetition here is not strange; it is straightforward and understandable.

A fully vocalized version would be:

يَحْزِمُ مِعْطَفًا وَاقِيًا مِنَ الْمَطَرِ لِكَيْ يَمْشِيَ فِي الْمَطَرِ.

This helps show:

• يَحْزِمُ = indicative verb
• مِعْطَفًا = accusative object
• وَاقِيًا = accusative adjective
• الْمَطَرِ = genitive after من and في
• يَمْشِيَ = subjunctive after لكي