Bitte geben Sie Ihre Adresse im Formular an.

Because the verb here is angeben, not plain geben.

• geben = to give
• angeben = to state, provide, enter, indicate

In this sentence, Bitte geben Sie Ihre Adresse im Formular an., the meaning is Please provide/state your address on the form.

So an is not a separate word with its own meaning here in the usual sense; it is the separable prefix of angeben.

Because angeben is a separable verb.

In many main clauses and commands, separable prefixes move to the end:

• infinitive: angeben
• command / main clause: geben ... an

So:

• Sie geben Ihre Adresse an.
• Bitte geben Sie Ihre Adresse an.

This is very common in German:

• anrufen → Ich rufe dich an.
• einkaufen → Wir kaufen heute ein.

Yes. This is the formal imperative.

German has different ways to give commands depending on who you are speaking to. With formal Sie, the imperative looks like this:

• geben Sie
• kommen Sie
• warten Sie

So Bitte geben Sie Ihre Adresse im Formular an. is a polite instruction or request.

Compare:

• Gib deine Adresse an. = informal, to one person
• Gebt eure Adresse an. = informal, to more than one person
• Geben Sie Ihre Adresse an. = formal, to one person or more than one person

Because they are the formal forms of you and your in German.

• Sie = formal you
• Ihre = formal your

These are always capitalized when they mean the polite/formal form.

Compare:

• sie = she / they
• ihre = her / their
• Sie = you (formal)
• Ihre = your (formal)

So capitalization is very important here.

It can be either.

Formal Sie is used for:

• one person in a polite/formal situation
• more than one person in a polite/formal situation

So the sentence could mean:

• Please provide your address on the form. — said to one person
• Please provide your address on the form. — said formally to multiple people, depending on context

The verb form stays the same: geben Sie.

Ihre Adresse is in the accusative case because it is the direct object of angeben.

You are providing what?
→ Ihre Adresse

So:

• nominative: Ihre Adresse
• accusative: Ihre Adresse

It looks the same here because Adresse is feminine, and the feminine possessive form does not change between nominative and accusative in this pattern.

You can see the case more clearly with a masculine noun:

• nominative: Ihr Name
• accusative: Ihren Namen

Example:

• Bitte geben Sie Ihren Namen an.

im is a contraction of in dem:

• in dem → im

So im Formular literally means in the form.

In natural English, this is often translated as on the form, because English usually says information is written on a form. German often uses in because the information goes into the fields or spaces of the form.

German usually thinks of a form as something with boxes or fields that information goes into, so in is very natural.

• im Formular = in the form

English often prefers on the form, but German commonly uses in in this context.

That said, in some contexts auf can appear with documents or pages, but for entering information into a form, im Formular sounds very normal.

The basic structure is:

• Bitte = please
• geben Sie = formal command
• Ihre Adresse = direct object
• im Formular = location/context
• an = separable prefix

So:

Bitte | geben Sie | Ihre Adresse | im Formular | an.

A key point is that the prefix an goes to the end because angeben is separable.

Also, German often places the object before the location phrase here, though other word orders may be possible depending on emphasis.

Yes.

• Geben Sie Ihre Adresse im Formular an. = a straightforward formal instruction
• Bitte geben Sie Ihre Adresse im Formular an. = more polite / softer

Bitte is very common in instructions, forms, signs, and customer service language.

Yes, depending on context.

A very common alternative is eintragen:

• Bitte tragen Sie Ihre Adresse im Formular ein.

This means something like Please enter/fill in your address on the form.

The difference is small in many situations:

• angeben = state/provide/indicate
• eintragen = enter/write into a form or field

Both are common, but eintragen can sound especially natural when talking about filling out a form.

If you are talking to one person informally, you would usually say:

• Bitte gib deine Adresse im Formular an.

Changes:

• geben Sie → gib
• Ihre → deine

If you are talking to several people informally:

• Bitte gebt eure Adresse im Formular an.

So the original sentence is specifically the formal version.

Adresse is pronounced approximately ah-DRESS-uh in standard German.

It is a borrowed word, ultimately from French, which is one reason it may look familiar to English speakers.

Its gender is feminine:

• die Adresse

So you get:

• Ihre Adresse
• meine Adresse
• die Adresse