Das Produkt ist weltweit bekannt.

Because Produkt is a neuter noun in German. Neuter singular nouns take das in the nominative case, so:

• das Produkt = the product

You have to learn the grammatical gender of each noun along with the noun itself.

It is in the nominative case because it is the subject of the sentence — the thing that is worldwide known.

In Das Produkt ist weltweit bekannt, the structure is:

• Das Produkt = subject
• ist = verb
• weltweit bekannt = description of the subject

In a normal German main clause, the finite verb usually comes in second position.

So the pattern here is:

• Das Produkt = first element
• ist = second element

This is one of the most important German word-order rules. Even if the first element is longer than one word, the finite verb still comes second.

Ist is the 3rd person singular form of sein in the present tense:

• ich bin
• du bist
• er / sie / es ist

Since das Produkt is singular and treated as it, the correct form is ist.

The sentence describes a state or condition, not an action. The product is worldwide known.

Here, bekannt is functioning as an adjective.

It describes the product:

• bekannt = known / well-known / famous

After verbs like sein, German often uses an adjective to describe the subject:

• Das Produkt ist bekannt.
• Das Haus ist groß.
• Der Film ist interessant.

So in this sentence, bekannt is best understood as a predicate adjective.

Because it comes after sein and is being used as a predicate adjective.

Predicate adjectives in German do not take adjective endings:

• Das Produkt ist bekannt.

But if the adjective comes before a noun, then it does take an ending:

• das bekannte Produkt = the well-known product

So compare:

• Das Produkt ist bekannt.
• das bekannte Produkt

Weltweit is an adverb here. It modifies bekannt and tells you the scope of how well-known the product is.

So:

• bekannt = known
• weltweit bekannt = known worldwide

It is not describing the noun directly here; it is modifying the adjective.

Because it modifies bekannt, and in German, adverbs often come before the adjective they modify.

So:

• weltweit bekannt = worldwide known / known worldwide

This is a very natural and common combination in German.

Yes. That would also be correct.

Compare:

• Das Produkt ist weltweit bekannt.
• Das Produkt ist auf der ganzen Welt bekannt.

They mean almost the same thing.
Weltweit is shorter and a bit more compact.
Auf der ganzen Welt is slightly more explicit and can sound a little more conversational.

Yes, German word order is somewhat flexible, but the finite verb still has to stay in second position in a main clause.

For example, you could say:

• Weltweit ist das Produkt bekannt.

This is grammatically correct, but it puts more emphasis on weltweit. The original sentence is the most neutral and natural version.

In a subordinate clause, the conjugated verb goes to the end.

For example:

• ..., weil das Produkt weltweit bekannt ist.
  = ... because the product is known worldwide.

So compare:

• Main clause: Das Produkt ist weltweit bekannt.
• Subordinate clause: ..., weil das Produkt weltweit bekannt ist.

They are very similar, but not always exactly identical in tone.

• weltweit bekannt = known worldwide
• weltbekannt = world-famous / globally famous

Weltbekannt is a single adjective and can sound a little stronger or more idiomatic.
Weltweit bekannt is slightly more literal: known across the world.

Both are common and correct.

You would change both the article and the verb:

• Die Produkte sind weltweit bekannt.

Changes:

• das Produkt → die Produkte
• ist → sind

Everything else stays the same.