Sie findet ihren Lippenstift nicht und sucht in jeder Tasche.

Because Lippenstift is masculine in German: der Lippenstift.

In this sentence, Lippenstift is the direct object of findet, so it has to be in the accusative case. A masculine accusative noun changes the possessive determiner:

• nominative: ihr Lippenstift
• accusative: ihren Lippenstift

So Sie findet ihren Lippenstift nicht uses ihren because the sentence is talking about finding the lipstick, not because the lipstick is the subject.

It is in the accusative case.

The verb finden normally takes a direct object, and the thing being found is that object:

• Sie findet was? → ihren Lippenstift

That is why the phrase is accusative. Since Lippenstift is masculine, the accusative form of ihr- becomes ihren.

In this sentence, nicht negates the idea of finding the lipstick.

German word order with nicht can be tricky, but here Sie findet ihren Lippenstift nicht is the natural way to say she can’t find her lipstick / she does not find her lipstick.

Compare:

• Sie findet ihren Lippenstift nicht. = She doesn’t find her lipstick.
• Sie findet nicht ihren Lippenstift. = It is not her lipstick that she finds (this sounds contrastive, as if she finds something else instead).

So the sentence uses the normal, neutral placement.

Because in here describes location, not movement toward a destination.

German two-way prepositions like in take:

• dative for location
• accusative for movement/direction

Here, she is searching in each bag, so the bags are the location of the search. That gives you dative:

• in jeder Tasche

If it were movement into each bag, you would use accusative:

• in jede Tasche

But that would mean something like into each bag, which is not the idea here.

Because Tasche is feminine, but it is in the dative singular after in.

The forms of jeder change by case and gender. For feminine singular:

• nominative: jede Tasche
• accusative: jede Tasche
• dative: jeder Tasche

So in jeder Tasche is correct because in is taking the dative here.

Yes. Sie can mean:

• she
• they
• you (formal singular or plural)

Only context tells you which one is meant.

One extra detail: at the beginning of a sentence, Sie is capitalized anyway, so you cannot tell from capitalization alone whether it is she/they or formal you. In the middle of a sentence:

• sie = she / they
• Sie = formal you

German often leaves out an object when it is already clear from the previous clause.

So:

• Sie findet ihren Lippenstift nicht und sucht in jeder Tasche.

is perfectly natural, because we already know what she is looking for: her lipstick.

You could also say:

• Sie findet ihren Lippenstift nicht und sucht ihren Lippenstift in jeder Tasche.

But that sounds more repetitive.

A more natural expanded version would be:

• Sie findet ihren Lippenstift nicht und sucht ihn in jeder Tasche.

where ihn refers back to Lippenstift.

Yes. German allows both patterns:

• etwas suchen = to look for something
• nach etwas suchen = to search for something

So these are both possible:

• Sie sucht ihren Lippenstift.
• Sie sucht nach ihrem Lippenstift.

In your sentence, the speaker does not use either object directly in the second clause, because it is already understood. Instead, the sentence focuses on where she is searching:

• in jeder Tasche

Because all nouns are capitalized in German.

So:

• der Lippenstift
• die Tasche

are capitalized no matter where they appear in the sentence. This is a standard feature of German spelling.

It is present tense, and in German the present tense often covers both English meanings:

• she searches
• she is searching

In this sentence, English would usually translate it as is searching because it describes what is happening right now.

So German Sie sucht can naturally correspond to English She is looking/searching.

Yes. Lippenstift is a compound noun:

• Lippe = lip
• Stift = stick, pen, pencil

German forms many nouns by combining smaller words into one longer word. The grammatical gender of the whole compound is usually determined by the last part, so because Stift is masculine (der Stift), der Lippenstift is also masculine.