In der Drogerie frage ich oft nach einem milden Duschgel, weil meine Haut empfindlich ist.

Because this sentence describes a location, not movement.

• in + dative = in/inside a place
• in + accusative = into a place

So:

• Ich bin in der Drogerie. = I am in the drugstore.
• Ich gehe in die Drogerie. = I am going into/to the drugstore.

Here, the speaker is already there, so in der Drogerie is correct.

German main clauses follow the verb-second rule: the finite verb must come in the second position.

Here, In der Drogerie is placed first for emphasis or context, so the verb comes next:

• In der Drogerie frage ich oft ...

If the subject came first, then you would get:

• Ich frage oft in der Drogerie ...

Both are possible, but the sentence given starts with the place phrase, so frage has to come before ich.

Because fragen can work in two different ways:

• jemanden fragen = to ask someone
• nach etwas fragen = to ask for/about something

In this sentence, the speaker is asking for a product, so German uses nach:

• nach einem milden Duschgel fragen

You could also combine both patterns:

• Ich frage die Verkäuferin nach einem milden Duschgel.

That means I ask the saleswoman for a mild shower gel.

Not exactly.

In this sentence, it is most naturally understood as fragen nach + dative, meaning to ask for/about something:

• Ich frage nach einem milden Duschgel.

There is also a verb nachfragen, but that usually means to ask again, to check, or to follow up.

So:

• Ich frage nach einem milden Duschgel. = I ask for a mild shower gel.
• Ich frage noch einmal nach. = I ask again / I follow up.

They are related, but they are not always interchangeable.

Because nach takes the dative case.

The noun is das Duschgel (neuter), so the indefinite article in the dative is einem:

• nominative/accusative: ein Duschgel
• dative: einem Duschgel

The adjective also has to match, so mild becomes milden:

• nach einem milden Duschgel

So the whole phrase is in the dative because of nach.

In German compounds, the last part determines the gender.

• das Gel = the gel
• therefore das Duschgel = the shower gel

That is why you get:

• ein mildes Duschgel in nominative/accusative
• einem milden Duschgel in dative

This is a very useful rule for compound nouns in German.

Because they are doing different jobs in the sentence.

In einem milden Duschgel, milden comes before a noun, so it is an attributive adjective. Attributive adjectives in German take endings.

But in meine Haut empfindlich ist, empfindlich comes after sein and describes the subject. That is a predicate adjective, and predicate adjectives do not take endings.

Compare:

• ein mildes Duschgel

• Das Duschgel ist mild.

• empfindliche Haut
• Meine Haut ist empfindlich.

Because weil introduces a subordinate clause, and in German subordinate clauses the finite verb usually goes to the end.

Main clause:

• Meine Haut ist empfindlich.

After weil:

• weil meine Haut empfindlich ist

This is one of the most important word-order rules in German.

Because German normally uses a comma before a subordinate clause, and weil introduces one.

So:

• ..., weil meine Haut empfindlich ist.

This comma is required in standard German.

Oft is an adverb of frequency, and it usually sits in the middle of the clause.

Here it appears naturally after the verb-subject part:

• In der Drogerie frage ich oft nach ...

If the sentence started with the subject, you could also say:

• Ich frage oft in der Drogerie nach einem milden Duschgel.

So oft is not completely fixed to one single spot, but it typically stays in the middle area of the sentence, not at the very end.

Meine Haut is natural because the speaker is talking about their own skin specifically.

German sometimes uses the definite article with body parts, but in this sentence meine Haut makes the meaning especially clear and personal.

A different but also natural version would be:

• ..., weil ich empfindliche Haut habe.

That means essentially the same thing, but the structure is different.

Using die Haut here would sound more general, almost like talking about skin in general rather than the speaker's own skin.

Not exactly.

A German Drogerie usually sells things like:

• shampoo
• shower gel
• cosmetics
• soap
• cleaning products

A place for medicine and prescriptions is usually an Apotheke.

So for Duschgel, Drogerie is exactly the right word. This is a common false-friend area for English speakers, because drugstore in English can overlap with both ideas.