Auf dem Tisch liegen Krümel vom Brot.

Because Krümel is plural here: crumbs.

The subject of the sentence is Krümel, and plural subjects take the plural verb form:

• der Krümel liegt = the crumb is lying
• die Krümel liegen = the crumbs are lying

So:

• Auf dem Tisch liegen Krümel vom Brot. = There are bread crumbs on the table / Bread crumbs are lying on the table

German main clauses usually put the finite verb in the second position.

Here, the sentence starts with the location phrase:

• Auf dem Tisch = on the table

That whole phrase takes the first position, so the verb must come next:

• Auf dem Tisch | liegen | Krümel vom Brot

The subject comes after the verb. This is normal German word order.

You could also say:

• Krümel vom Brot liegen auf dem Tisch.

That is also correct, just with a different emphasis.

Because this sentence describes location, not movement.

With auf, German uses:

• dative for location: on the table
• accusative for direction/movement: onto the table

So:

• auf dem Tisch = on the table
• auf den Tisch = onto the table

Compare:

• Auf dem Tisch liegen Krümel. = Crumbs are lying on the table.
• Ich lege die Krümel auf den Tisch. = I put the crumbs onto the table.

It is dative singular.

The noun is der Tisch. After auf in a location meaning, it becomes dative:

• nominative: der Tisch
• dative: dem Tisch

So auf dem Tisch literally means on the table.

vom is a contraction of von dem.

• von = from, of
• dem = the (dative masculine/neuter)

So:

• vom Brot = von dem Brot

In natural German, vom is much more common than von dem here.

Because German often uses the definite article where English might not.

Here vom Brot means something like:

• from the bread
• of the bread

It refers to some specific bread in the situation, even if English would simply say bread crumbs.

German often prefers an article in these kinds of phrases:

• der Geruch vom Kaffee = the smell of the coffee / coffee smell
• die Farbe vom Auto = the color of the car

So Krümel vom Brot is very natural.

Because German often leaves out the article with an indefinite plural.

Compare:

• ein Krümel = a crumb
• Krümel = crumbs / some crumbs

So Krümel here means some crumbs or just crumbs.

If you wanted to make them definite, you could say:

• Die Krümel vom Brot liegen auf dem Tisch. = The bread crumbs are on the table.

Krümel is in the nominative plural, because it is the subject of the sentence.

Even though it comes after the verb, it is still the subject.

Structure:

• Auf dem Tisch = prepositional phrase
• liegen = verb
• Krümel vom Brot = subject

A common mistake for English speakers is to assume the first noun phrase must be the subject. In German, that is not true.

German often uses position verbs like:

• liegen = lie
• stehen = stand
• sitzen = sit

These are very common when talking about where things are.

So:

• Auf dem Tisch liegen Krümel. = There are crumbs on the table. / Crumbs are lying on the table.

You could sometimes hear:

• Auf dem Tisch sind Krümel.

That is understandable, but liegen sounds more idiomatic and more precise, because crumbs are things that lie on a surface.

Almost, yes.

• Krümel vom Brot = crumbs from the bread
• Brotkrümel = bread crumbs

Brotkrümel is a compound noun and is often the more compact way to say it.

So these are both possible:

• Auf dem Tisch liegen Krümel vom Brot.
• Auf dem Tisch liegen Brotkrümel.

The first version can feel a little more connected to a particular loaf or piece of bread in the situation.

Because all nouns are capitalized in German.

So in this sentence:

• Tisch is capitalized because it is a noun
• Krümel is capitalized because it is a noun
• Brot is capitalized because it is a noun

This is always true in standard German spelling.

Yes, Krümel can look the same in singular and plural.

• singular: der Krümel
• plural: die Krümel

You can tell which one it is from the article or the verb:

• Der Krümel liegt auf dem Tisch. = The crumb is on the table.
• Krümel liegen auf dem Tisch. = Crumbs are on the table.

In your sentence, liegen clearly shows that Krümel is plural.

Yes, absolutely.

That version is also natural:

• Es liegen Krümel vom Brot auf dem Tisch.

This es is not really a normal subject with meaning; it is more like introductory there in English:

• There are bread crumbs on the table.

Both are correct:

• Auf dem Tisch liegen Krümel vom Brot.
• Es liegen Krümel vom Brot auf dem Tisch.

The first one emphasizes the location more strongly by putting it first.