يحمل بوصلة وطارد حشرات لكي يتنزه قرب البحيرة.

Because Arabic often builds the subject into the verb itself.
يحمل already means he carries or he is carrying.

So the sentence does not need هو. You could add هو for emphasis, but in normal Arabic it is usually omitted:

• يحمل... = He carries / is carrying...
• هو يحمل... = He is carrying... with extra emphasis on he

The Arabic imperfect tense often covers both:

• a simple present meaning: he carries
• a present continuous meaning: he is carrying

Context tells you which one sounds better in English. Arabic does not always force the same distinction English does.

Arabic does not have an indefinite article like English a/an.

Instead, indefiniteness is usually shown by:

• the absence of الـ
• and, in fully vocalized Arabic, often tanwīn at the end

So:

• بوصلة = a compass
• البوصلة = the compass

The same idea applies to طارد حشرات: it is indefinite here, so it means an insect repellent or insect repellent.

It is a noun phrase meaning insect repellent, literally something like a repeller of insects.

A helpful way to understand it is as an iḍāfa-like compound:

• طارد = repeller / repelling thing
• حشرات = insects

So together:

• طارد حشرات = insect repellent

English often uses a singular noun before another noun, as in insect repellent, but Arabic commonly expresses that relationship differently.

Because Arabic is expressing the meaning repellent for insects.

• حشرة = an insect
• حشرات = insects

Using the plural is very natural here because the product is meant to repel insects in general, not just one insect.

Because they are both direct objects of يحمل.

The structure is:

• يحمل = he carries
• بوصلة = a compass
• و = and
• طارد حشرات = insect repellent

So Arabic is simply saying: He carries [a compass] and [insect repellent].

لكي means so that or in order to. It introduces a purpose.

So:

• لكي يتنزه = so that he can take a walk / in order to go for a walk

It tells you why he is carrying those things.

Because لكي is followed by a verb expressing the intended action or purpose.

The base verb is:

• تنزّه = to stroll, take a walk, go for an outing

Its imperfect form is:

• يتنزه = he strolls / he takes a walk / he goes for a walk

After لكي, the verb is normally in the subjunctive. In fully vocalized Arabic, that would be shown at the end:

• لكي يتنزَّهَ

In ordinary unvocalized writing, you often just see يتنزه.

It means near the lake.

• قرب = near / close to
• البحيرة = the lake

So:

• قرب البحيرة = near the lake

Here قرب functions like an adverb or location word. Arabic can also express this idea with:

• بالقرب من البحيرة = near the lake

Both are natural, but قرب البحيرة is shorter and very common.

Because البحيرة is definite: the lake.

• بحيرة = a lake
• البحيرة = the lake

So the sentence is talking about a specific or contextually known lake, not just any lake.

In normal Arabic writing, short vowels and many case endings are usually omitted.

So the sentence is written simply as: يحمل بوصلة وطارد حشرات لكي يتنزه قرب البحيرة

But if you added the grammatical endings, it could be read roughly as: يحملُ بوصلةً وطاردَ حشراتٍ لكي يتنزَّهَ قربَ البحيرةِ

Those endings show things like:

• the verb ending
• the direct objects
• the purpose clause
• the genitive after قرب

Learners should know they exist, even though they are often not written in everyday text.

Yes, by default it is understood to be the same person: he.

So the meaning is:

• He carries a compass and insect repellent in order to take a walk near the lake.

Arabic often leaves that connection implicit instead of repeating the pronoun.