Zu Hause klappe ich den Laptop auf und lese die E-Mail.

Because German main clauses follow the verb-second rule. The finite verb must be in the second position, not necessarily the second word.

In Zu Hause klappe ich den Laptop auf, the first position is taken by Zu Hause, so the verb klappe comes next, and ich follows after it.

So the structure is:

• Zu Hause = position 1
• klappe = position 2
• ich = subject after the verb

This is very normal in German whenever you begin with a time or place expression.

Because the verb is aufklappen, which is a separable verb. In a main clause, the prefix separates and moves to the end.

So:

• infinitive: aufklappen
• main clause: ich klappe den Laptop auf

You will see the full verb stay together in other structures, for example:

• Ich will den Laptop aufklappen.
• ..., weil ich den Laptop aufklappe.

This is one of the most important German verb patterns to learn.

Here aufklappen means something like to flip open or to open up something that folds or has a lid.

With Laptop, it means opening it by lifting the screen. In English, you would often just say open the laptop, but German commonly uses the more specific verb aufklappen.

Because Laptop is a masculine noun: der Laptop.

In this sentence, it is the direct object of aufklappen, so it must be in the accusative case:

• nominative: der Laptop
• accusative: den Laptop

That change from der to den is very common with masculine nouns.

In standard German, E-Mail is usually feminine:

• die E-Mail

Here it is also a direct object, but feminine singular looks the same in nominative and accusative:

• nominative: die E-Mail
• accusative: die E-Mail

So unlike der Laptop → den Laptop, there is no visible article change here.

There are some regional differences, but die E-Mail is the standard form learners should use.

Because zu Hause means at home: it describes location.

Nach Hause means home / to home: it describes movement toward home.

Compare:

• Zu Hause lese ich. = I read at home.
• Ich gehe nach Hause. = I go home.

In your sentence, the person is already at home, so Zu Hause is correct.

Zu Hause is a fixed expression. The form Hause is an old dative form that survives in this phrase.

You do not usually build new phrases with Hause. It is best to learn zu Hause as one unit meaning at home.

It is capitalized because it comes from the noun Haus.

Yes. As an adverb, both zu Hause and zuhause are accepted in modern German.

The two-word spelling is very common and looks completely natural here.

Do not confuse this with the noun das Zuhause, which means something like home in the sense of one’s home environment or a place where someone feels at home.

Because the subject is the same in both parts of the sentence, German can leave it out in the second part.

So these are both possible:

• Zu Hause klappe ich den Laptop auf und lese die E-Mail.
• Zu Hause klappe ich den Laptop auf und ich lese die E-Mail.

The version without the second ich is usually more natural and smoother.

Yes, that is grammatical.

The difference is mainly emphasis:

• Zu Hause klappe ich ... emphasizes at home
• Ich klappe zu Hause ... starts more neutrally with the subject

German often moves time or place expressions to the front when they are the part the speaker wants to highlight.

They are both in the present tense.

In German, the present tense can express:

• something happening now
• a habitual action
• a general description
• sometimes even a near future action

So this sentence could describe what the speaker is doing now, or it could describe a usual routine, depending on context.

German often uses the definite article where English would prefer a possessive like my.

If it is obvious from the situation whose laptop or which email is meant, den Laptop and die E-Mail can sound perfectly natural.

If you want to make the ownership explicit, you can absolutely say:

• meinen Laptop
• meine E-Mail

So the sentence with possessives would also be possible; it would just sound a little more specific.

That is the standard German spelling: E-Mail.

German often keeps or uses a hyphen in words of this type, and since all nouns are capitalized in German, both parts look capitalized here.

So E-Mail is simply the normal written form you should learn and use.