Mein Koffer liegt noch auf dem Gepäckband.

Because Koffer is masculine singular here: der Koffer.

The possessive word mein works a lot like ein. In the nominative masculine singular, it usually has no ending:

• mein Koffer = my suitcase

Compare:

• mein Koffer → masculine
• meine Tasche → feminine
• mein Gepäck → neuter
• meine Koffer → plural

So meine Koffer would mean my suitcases, not my suitcase.

Because mein already functions as a determiner. In German, you normally do not use an article together with a possessive in this kind of phrase.

So you say:

• mein Koffer
• not der mein Koffer

This is similar to English: we say my suitcase, not the my suitcase.

German often prefers a position verb where English would simply use to be.

Here, liegen means to be lying / to be located in a lying position. For objects like a suitcase resting on a baggage belt, liegen is very natural.

So:

• Mein Koffer liegt ... = My suitcase is lying / is still on ...

You can sometimes hear ist in everyday speech, but liegt is more idiomatic because it describes the suitcase’s position.

Related position verbs:

• liegen = to lie
• stehen = to stand
• sitzen = to sit
• hängen = to hang

Because the subject is mein Koffer, 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 Koffer is singular, you need liegt.

Here noch means still.

So the sentence suggests that the suitcase has not been picked up yet and remains on the baggage belt.

Common meanings of noch include:

• still → Er ist noch hier.
• yet / another / one more, depending on context

In this sentence, still is the right idea.

That is the most natural position in a normal main clause here.

German often puts adverbs like noch in the middle field of the sentence, usually after the verb and before longer phrases such as prepositional phrases.

So this sounds natural:

• Mein Koffer liegt noch auf dem Gepäckband.

You could move things around for emphasis, but the neutral version is the one above.

For example:

• Noch liegt mein Koffer auf dem Gepäckband.
  This is possible, but it puts special emphasis on noch.

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

• dative for location: where something is
• accusative for direction/movement toward a destination: where something is going

Here the suitcase is already located on the belt, so German uses the dative:

• auf dem Gepäckband = on the baggage belt

Compare:

• Der Koffer liegt auf dem Gepäckband.
  location → dative
• Ich stelle den Koffer auf das Gepäckband.
  movement onto it → accusative

Because Gepäckband is neuter: das Gepäckband.

With the preposition auf expressing location, you need the dative singular, and the dative form of das is dem:

• nominative: das Gepäckband
• dative: dem Gepäckband

So:

• auf dem Gepäckband

• der Koffer → masculine
• das Gepäckband → neuter

That matters because it affects words around them:

• mein Koffer
• auf dem Gepäckband

It is a good idea to learn German nouns together with their articles:

• der Koffer
• das Gepäckband

It is a compound noun:

• Gepäck = luggage
• Band = belt / conveyor belt / strip

So Gepäckband means baggage belt or luggage conveyor belt, especially at an airport.

A useful rule for German compounds: the last part determines the gender.

Since Band is neuter (das Band), the whole word is also neuter:

• das Gepäckband

Because German main clauses normally follow the verb-second rule: the finite verb comes in the second position.

Here:

1. Mein Koffer
2. liegt

Then the rest follows:

• noch
• auf dem Gepäckband

So the structure is:

• Subject + finite verb + other elements

You could also put another element first, but then the verb still stays second:

• Noch liegt mein Koffer auf dem Gepäckband.
• Auf dem Gepäckband liegt mein Koffer noch.

Those versions are possible, but the original sentence is the most neutral.

Yes. Koffer is one of those German nouns whose singular and plural look the same:

• singular: der Koffer
• plural: die Koffer

You tell the difference from the article or from the rest of the sentence:

• mein Koffer liegt → singular
• meine Koffer liegen → plural

In your sentence, mein and liegt clearly show it is singular.

Yes, that would be understandable, and many learners might say it first. But liegt is usually better and more natural in German because it expresses the suitcase’s physical position.

So:

• Mein Koffer ist noch auf dem Gepäckband. → understandable
• Mein Koffer liegt noch auf dem Gepäckband. → more idiomatic

German often likes to be more specific than English about how something is positioned.