Ihr roter Lippenstift passt gut zu der neuen Bluse.

At the beginning of a sentence, all first words are capitalized, so Ihr does not automatically mean formal your here.

Depending on context, ihr/Ihr could mean:

• her
• their
• your (formal)

Because it is sentence-initial, you need the wider context to know which one is meant. If this word appeared in the middle of a sentence, capitalization could help distinguish Ihr = formal your from ihr = her/their.

Because Lippenstift is masculine singular and it is the subject of the sentence.

After a possessive word like ihr, the adjective has to show the grammatical ending. For a masculine nominative singular noun, that ending is -er:

• ihr roter Lippenstift
• ein roter Lippenstift

So roter is the correct form.

Yes. The noun is:

• der Lippenstift = lipstick

That means it is masculine.

In this sentence, you can also tell from:

• roter → masculine nominative singular adjective ending
• passt → singular verb form, agreeing with Lippenstift

Also, Lippenstift is a compound noun:

• Lippe = lip
• Stift = stick, pencil

German often combines nouns into one word.

Because the subject is singular:

• Ihr roter Lippenstift = one lipstick

So the verb must be third person singular:

• passen = infinitive
• passt = it matches / it goes

If the subject were plural, you would use passen:

• Ihre roten Lippenstifte passen gut ...

This is a very common German structure:

• zu etwas passen = to go with something / to match something

So here:

• passt ... zu der neuen Bluse = goes well with the new blouse

And:

• gut is an adverb meaning well

So passt gut zu means matches well with or goes well with.

Because the verb passen often uses the preposition zu when you mean match / go with.

Compare:

• Der Lippenstift passt zu der Bluse.
  = The lipstick matches the blouse.

Without zu, passen often has a different meaning, such as to fit in size or suitability:

• Die Bluse passt mir.
  = The blouse fits me.

So in this sentence, zu is necessary because the idea is matching, not physical fit.

The preposition zu always takes the dative case.

The noun is:

• die Bluse = nominative
• der Bluse = dative

So:

• zu der Bluse
• zu der neuen Bluse

That is why you see der, not die.

Because the adjective is in the dative feminine after a definite article.

Here is the pattern:

• die neue Bluse = nominative feminine
• zu der neuen Bluse = dative feminine

After der in this dative form, the adjective takes -en:

• neuen

So zu der neuen Bluse is correct.

Yes. zur is just the contraction of zu der:

• zu der neuen Bluse
• zur neuen Bluse

Both are correct. In everyday German, zur neuen Bluse is often more natural and more common in speech.

The structure is:

• Ihr roter Lippenstift = subject
• passt = verb
• gut = adverb
• zu der neuen Bluse = prepositional phrase

So the sentence follows normal main-clause word order in German:

• subject + verb + other elements

German main clauses usually place the finite verb in second position, and that is exactly what happens here.

Because all German nouns are capitalized.

So:

• Lippenstift
• Bluse

are capitalized simply because they are nouns. This is one of the most noticeable spelling rules in German.

No, not in this sentence.

Here, passen zu means:

• to match
• to go with

If you want to talk about clothing size or fit on the body, German also uses passen, but in a different pattern:

• Die Bluse passt mir. = The blouse fits me.
• Der Schuh passt nicht. = The shoe does not fit.

So:

• passen zu = match / go with
• passen without zu can mean fit

That is an important distinction.