Im Federmäppchen meiner Nichte liegen zwei Buntstifte und ein kleiner Spitzer.

Im is a contraction of in dem.

• in = in
• dem = the dative singular form of the for a masculine or neuter noun

So im Federmäppchen literally means in the pencil case.

German very often contracts preposition + article:

• in dem → im
• an dem → am
• zu dem → zum

Both in dem and im are possible in theory, but im is the normal form here.

Because this sentence describes location, not movement.

• im Federmäppchen = in the pencil case / inside it
• ins Federmäppchen = into the pencil case

German uses:

• dative after in for location
• accusative after in for direction or movement toward something

So:

• Im Federmäppchen liegen zwei Buntstifte. = The pencils are in the pencil case.
• Ich lege zwei Buntstifte ins Federmäppchen. = I put two colored pencils into the pencil case.

Because Mäppchen ends in -chen, and nouns ending in -chen are always neuter in German.

So it is:

• das Federmäppchen
• im Federmäppchen = in the pencil case

This is useful to remember: diminutive endings like -chen and -lein always make nouns neuter.

Examples:

• das Mädchen
• das Häuschen
• das Büchlein

Because meiner Nichte is in the genitive, showing possession.

The phrase means:

• das Federmäppchen meiner Nichte
• literally: the pencil case of my niece
• natural English: my niece’s pencil case

Here meiner is the genitive feminine form of mein to match Nichte, which is a feminine noun:

• meine Nichte = my niece
• meiner Nichte = of my niece

So the sentence is not talking about my niece as a separate object in the sentence; it is using her to show whose pencil case it is.

Because feminine nouns in the singular usually do not add an extra genitive ending.

In German, the genitive is often shown mainly by the article or determiner:

• die Nichte = the niece
• meiner Nichte = of my niece

Compare that with many masculine or neuter nouns, which often do add -s or -es in the genitive:

• der Bruder → des Bruders
• das Kind → des Kindes

But feminine nouns usually stay the same:

• die Schwester → der Schwester
• die Nichte → meiner Nichte

German often uses position verbs where English would simply use to be.

liegen literally means to lie, but in sentences like this it often means that objects are lying/resting somewhere.

So:

• Im Federmäppchen liegen zwei Buntstifte ...
• more literally: In the pencil case lie two colored pencils ...
• natural English: There are two colored pencils ... in the pencil case

This is very normal German. Other common position verbs are:

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

For small loose objects in a pencil case, liegen is very natural.

Because German main clauses follow the verb-second rule.

The first element in the sentence is:

• Im Federmäppchen meiner Nichte

That whole phrase takes the first position. Once something is placed first, the finite verb must come next:

• Im Federmäppchen meiner Nichte liegen ...

So the subject comes after the verb here.

A more basic word order would be:

• Zwei Buntstifte und ein kleiner Spitzer liegen im Federmäppchen meiner Nichte.

Both are correct. The original sentence just puts the location first for emphasis or flow.

The subject is:

• zwei Buntstifte und ein kleiner Spitzer

This is a compound subject joined by und, so it is treated as plural.

That is why the verb is:

• liegen = plural

Even though ein kleiner Spitzer is singular by itself, the full subject is:

• two colored pencils + one small sharpener

Together, that makes more than one thing, so the verb must be plural.

Because ein kleiner Spitzer is in the nominative masculine singular.

It is part of the subject of the sentence, so it must be nominative.

• der Spitzer = the sharpener
• ein kleiner Spitzer = a small sharpener

After ein, adjectives take mixed endings. For a masculine nominative singular noun, the adjective ending is -er:

• ein kleiner Spitzer

You would get kleinen in other cases, for example accusative masculine:

• Ich sehe einen kleinen Spitzer.

Because after a number, German usually does not use an article unless there is a special reason.

So:

• zwei Buntstifte = two colored pencils

That is the normal way to say it.

You would not usually say die zwei Buntstifte unless you mean the two colored pencils, referring to specific ones already known from context.

Compare:

• zwei Buntstifte = two colored pencils
• die zwei Buntstifte = the two colored pencils

Yes. Der Spitzer is a normal word for a pencil sharpener, especially the small kind used in school.

So:

• ein kleiner Spitzer = a small pencil sharpener

You may also see Anspitzer, which can mean the same thing. In everyday school-related German, Spitzer is very common.

Because all nouns are capitalized in German.

That is a standard spelling rule, not a special feature of this sentence.

So in this sentence, the nouns are:

• Federmäppchen
• Nichte
• Buntstifte
• Spitzer

Words like im, meiner, liegen, zwei, und, ein, kleiner are not nouns, so they are not capitalized.

Yes, you can, and people will understand it:

• im Federmäppchen von meiner Nichte

But im Federmäppchen meiner Nichte is more standard and stylistically better, especially in writing.

So:

• meiner Nichte = genitive possession, more elegant/standard
• von meiner Nichte = common in speech, but less formal

Both mean the same thing. For learners, it is useful to understand both, but the version in your sentence is a very good model.