Mein Arm liegt auf dem Tisch.

Because Arm is a masculine singular noun in the nominative case here.

The subject of the sentence is mein Arm, and for a masculine singular noun in the nominative, the possessive word is mein.

A quick comparison:

• mein Arm = my arm
• meine Hand = my hand

So the form changes depending on the gender and case of the noun.

In German, all nouns are capitalized, not just proper names.

So:

• Arm
• Tisch
• Haus
• Katze

This is one of the first big spelling differences English speakers notice in German.

German often uses special position/location verbs where English might just use is.

Here, liegen means to lie or to be lying. It is used for things that are in a horizontal position.

So German prefers:

• Der Stift liegt auf dem Tisch.
• Mein Arm liegt auf dem Tisch.

rather than using sein (to be).

Related verbs:

• liegen = to lie, be lying
• stehen = to stand, be standing
• sitzen = to sit, be sitting

So liegt sounds natural because an arm is understood as resting in a lying position.

Because the subject is mein Arm, which is third-person singular.

The verb liegen is conjugated like this in the present tense:

• ich liege
• du liegst
• er/sie/es liegt
• wir liegen
• ihr liegt
• sie/Sie liegen

Since Arm is singular, you use liegt.

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

You can find the subject by asking: What is lying on the table? Answer: mein Arm

So:

• mein Arm = nominative subject

Because this sentence describes location, not movement.

The preposition auf can take either:

• dative for location: on / on top of
• accusative for movement toward a place: onto

So:

• Mein Arm liegt auf dem Tisch. = My arm is on the table.
  → location → dative
• Ich lege meinen Arm auf den Tisch. = I put my arm onto the table.
  → movement/direction → accusative

This is a very common German pattern with so-called two-way prepositions.

Because Tisch is a masculine noun, and after auf in a location meaning, you need the dative case.

The masculine dative singular article is dem.

So:

• nominative: der Tisch
• accusative: den Tisch
• dative: dem Tisch

That is why the sentence has auf dem Tisch.

Often, yes, but not always exactly in the same way as English on.

In this sentence, auf means on in the sense of on top of a surface:

• auf dem Tisch = on the table

German prepositions do not always match English one-for-one in every context, so it is best to learn them in phrases.

For example:

• auf dem Tisch = on the table
• an der Wand = on the wall
• im Bett = in bed

So auf is correct here because a table is a surface.

Yes. German word order is flexible as long as the conjugated verb stays in second position in a normal main clause.

You can say:

• Mein Arm liegt auf dem Tisch.
• Auf dem Tisch liegt mein Arm.

Both are correct.

The second version puts more emphasis on where the arm is.

What does not change is that liegt stays in the second position of the clause.

Because mein already functions like a determiner, similar to an article.

In German, you normally say:

• mein Arm
• dein Arm
• sein Arm

not:

• der mein Arm ✘

So mein already fills the slot where an article like der would go.

Yes, it is grammatical and natural.

It could be used in a situation where someone’s arm is physically resting on the table.

For example:

• A doctor notices your posture.
• Someone tells you to move your arm.
• You are describing a scene or body position.

It may sound slightly unusual by itself only because it is very specific, not because the German is wrong.

Sometimes, yes. German often uses body parts a little differently from English, especially when the owner is already clear.

For example, German may sometimes prefer an article in other structures:

• Ich hebe den Arm. = I raise my arm.
• Er hat die Hand auf dem Tisch. = He has his hand on the table.

But in your sentence, mein Arm is completely correct and clear. It simply makes the ownership explicit.

A rough English-friendly guide is:

mine arm leekt owf daym tish

A few notes:

• mein sounds like English mine
• liegt has a long ie sound, like lee-gt, though the g is softened at the end
• auf sounds a bit like owf
• dem has a long e, roughly daym
• Tisch sounds like tish

A more approximate IPA pronunciation is:

[maɪn aʁm liːkt aʊf deːm tɪʃ]

The structure is:

Subject + verb + prepositional phrase

So here:

• Mein Arm = subject
• liegt = verb
• auf dem Tisch = prepositional phrase showing location

This is a very common and useful German sentence pattern.