Das Einkaufszentrum öffnet früh.

Because Einkaufszentrum is a neuter noun in German, so it takes the article das.

A useful clue is the last part of the compound noun:

• das Zentrum = the center

In German compound nouns, the last part usually determines the grammatical gender of the whole word. Since Zentrum is neuter, Einkaufszentrum is also neuter:

• das Zentrum
• das Einkaufszentrum

German often combines smaller words into compound nouns.

Here, Einkaufszentrum is made from:

• der Einkauf = shopping / purchase
• das Zentrum = center

So the whole noun means a shopping center or shopping mall.

This is very normal in German. Instead of separating words like English often does, German usually joins them into one noun.

It is in the nominative case because it is the subject of the sentence — the thing doing the action.

In Das Einkaufszentrum öffnet früh:

• das Einkaufszentrum = subject
• öffnet = verb
• früh = adverb

So the mall/shopping center is the thing that opens.

Because German main clauses usually follow the verb-second rule.

In a normal statement, the finite verb goes in position 2:

• Das Einkaufszentrum | öffnet | früh

Even if you move another element to the front, the verb still stays second:

• Früh öffnet das Einkaufszentrum.

That sounds more marked or stylistic, but it is still correct.

Because öffnet is the conjugated form of the verb öffnen.

The subject is das Einkaufszentrum, which is third person singular (it), so the verb takes the -t ending:

• ich öffne
• du öffnest
• er/sie/es öffnet
• wir öffnen
• ihr öffnet
• sie/Sie öffnen

Since das Einkaufszentrum is grammatically like es, you use öffnet.

Here, früh is an adverb, because it describes when the opening happens.

It answers the question:

• Wann öffnet das Einkaufszentrum?
• Früh.

German often uses the same word as both an adjective and an adverb:

• ein früher Termin = an early appointment (adjective)
• Das Einkaufszentrum öffnet früh. = The shopping center opens early (adverb)

Because in German, nouns are capitalized, but adverbs are not.

So:

• das Einkaufszentrum → Einkaufszentrum is capitalized because it is a noun
• früh is not capitalized because it is an adverb

Compare:

• der frühe Morgen = the early morning
• morgens früh = early in the morning

The tricky parts are the vowels with umlauts:

• ö in öffnet sounds somewhat like the vowel in French peur or like the vowel in British English bird, but with rounded lips
• ü in früh is made by saying something like ee while rounding your lips

A rough guide:

• öffnet ≈ URFF-net / OEFF-net
• früh ≈ a rounded free, but with the German ü sound

Also:

• the h in früh is not strongly pronounced by itself; it mainly shows that the vowel is long

Often, yes — both can mean to open.

But there is a small style difference:

• öffnen is a bit more neutral or formal
• aufmachen is more everyday and conversational

So you could also hear:

• Das Einkaufszentrum macht früh auf.

That is very natural in spoken German.

Yes, depending on context, früh can suggest either:

• early in general
• early in the day

In this sentence, it most naturally means early — probably earlier than usual or early in the morning, depending on context.

If you want to be more specific, German can say:

• früh am Morgen = early in the morning
• sehr früh = very early

Yes, but it means something slightly different in feel.

• Das Einkaufszentrum öffnet früh.
  This focuses on the action/event of opening.

• Das Einkaufszentrum ist früh geöffnet.
  This focuses more on the state/result of being open early.

The first sentence is simpler and more natural if you just want to state the opening time pattern.

Because German does not need a helper verb like does in a normal present-tense statement.

English:

• The shopping center opens early.

German:

• Das Einkaufszentrum öffnet früh.

The main verb öffnet already carries the tense and agreement, so no extra word is needed.

Yes, if the noun has already been mentioned.

You could say:

• Es öffnet früh.

Because das Einkaufszentrum is neuter, the matching pronoun is es.

But if you say Es öffnet früh by itself with no context, it may be unclear what es refers to.