Das Zeugnis liegt auf dem Tisch.

Because Zeugnis is a neuter noun in German, so its basic article is das: das Zeugnis.

Unfortunately, noun gender in German often just has to be learned with the noun. That said, many nouns ending in -nis are neuter, for example:

• das Zeugnis
• das Ergebnis
• das Erlebnis

So the best habit is to learn the word together with its article: das Zeugnis.

Zeugnis can mean a few related things depending on context. Common meanings include:

• a school report or report card
• a certificate
• a testimonial or reference from an employer

In this sentence, it usually sounds like a physical document lying on the table.

German often prefers specific position verbs where English might simply use is.

• liegen = to lie, to be lying, to be located horizontally
• stehen = to stand, to be standing vertically
• sitzen = to sit

So Das Zeugnis liegt auf dem Tisch is more natural than just saying it is on the table, because a document is thought of as lying flat.

Compare:

• Das Buch liegt auf dem Tisch. = The book is lying on the table.
• Die Flasche steht auf dem Tisch. = The bottle is standing on the table.

Because auf is a two-way preposition. That means it can take:

• dative for location
• accusative for movement toward a destination

Here, the sentence describes where the document already is, so German uses the dative:

• auf dem Tisch = on the table

If it were moving onto the table, you would use the accusative:

• Ich lege das Zeugnis auf den Tisch. = I put the certificate/report on the table.

So:

• wo? where? → dative → auf dem Tisch
• wohin? to where? → accusative → auf den Tisch

Tisch is masculine, so the basic form is der Tisch. But after auf in a location meaning, the noun goes into the dative case. The masculine dative article is dem.

So:

• nominative: der Tisch
• dative: dem Tisch

That is why the sentence has auf dem Tisch.

Yes, absolutely. That is also correct.

German word order is flexible, but the finite verb still has to stay in the second position in a normal statement.

So both are correct:

• Das Zeugnis liegt auf dem Tisch.
• Auf dem Tisch liegt das Zeugnis.

The difference is mainly emphasis:

• Das Zeugnis liegt auf dem Tisch. → neutral
• Auf dem Tisch liegt das Zeugnis. → emphasizes the location

In a normal German main clause, the conjugated verb usually comes in position 2. This is often called the V2 rule.

In your sentence:

• Das Zeugnis = position 1
• liegt = position 2
• auf dem Tisch = the rest

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

• Auf dem Tisch = position 1
• liegt = position 2
• das Zeugnis = after that

So the verb’s position is very important in German sentence structure.

It can express both ideas.

German simple present often covers both:

• lies
• is lying

So Das Zeugnis liegt auf dem Tisch can naturally mean:

• The report is on the table.
• The report is lying on the table.

German does not need a separate progressive form like English is lying in most everyday sentences.

In German, all nouns are capitalized. So:

• Zeugnis is capitalized because it is a noun
• Tisch is capitalized because it is a noun

Das is capitalized here because it is the first word of the sentence. If it appeared in the middle of a sentence as an article, it would normally be lowercase:

• Ich sehe das Zeugnis.

So noun capitalization is a regular feature of German spelling.

Yes, but it sounds more formal or neutral, and less natural in everyday speech for a simple object on a table.

• Das Zeugnis liegt auf dem Tisch. = natural, everyday German
• Das Zeugnis befindet sich auf dem Tisch. = more formal, more like is located on the table

For ordinary conversation, liegt is the better choice here.

Yes. Das here can be understood as the in English, so it refers to a specific certificate/report that is known from the context.

If you wanted an indefinite meaning, you could say:

• Ein Zeugnis liegt auf dem Tisch. = A certificate/report is lying on the table.

So das Zeugnis suggests a particular document, not just any one.