Królik też ma długie pazury, ale jest bardzo spokojny.

Też means too / also. In Polish, it is often placed near the word or idea it adds to.

So Królik też ma długie pazury suggests the rabbit also has long claws.

If you move też, the emphasis can shift a little:

• Królik też ma długie pazury = the rabbit also has long claws
• Królik ma też długie pazury = the rabbit has long claws too

Both are possible, but the version in your sentence sounds very natural.

Polish usually drops subject pronouns when they are not needed.

The verb forms already tell you the person:

• ma = he/she/it has
• jest = he/she/it is

So Królik ma... is enough. Adding on would usually sound emphatic:

• On jest bardzo spokojny = he is very calm

In normal sentences, Polish prefers to leave the pronoun out.

Because długie has to agree with pazury.

Pazury is:

• plural
• non-masculine-personal

So the adjective also takes the plural non-masculine-personal form:

• długi = singular masculine
• długie = plural non-masculine-personal

That is why you get długie pazury.

Because pazury is the direct object of ma.

The verb mieć (to have) takes the accusative case. But with many non-masculine-personal plurals, the accusative looks exactly the same as the nominative.

So:

• nominative plural: pazury
• accusative plural: pazury

That is why the form does not change here.

For comparison:

• genitive plural: pazurów
• instrumental plural: pazurami

Because spokojny is an adjective, and here it describes the rabbit.

After jest (is), Polish normally uses an adjective:

• jest spokojny = he/it is calm

Spokojnie is an adverb, meaning calmly / quietly, and it describes how something is done:

• mówi spokojnie = he speaks calmly

So in this sentence, spokojny is correct.

Because królik is a grammatically masculine noun.

In Polish, adjectives must agree with the noun in gender and number:

• spokojny = masculine singular
• spokojna = feminine singular
• spokojne = neuter singular or non-masculine-personal plural

Since the noun is królik, the adjective must be spokojny.

Usually no, not in a normal standard sentence like this.

In Polish present-tense sentences with to be, you normally keep jest:

• Królik jest bardzo spokojny

So unlike some other Slavic languages, standard Polish does not usually drop the present tense of być in ordinary statements.

Ale means but and introduces a clear contrast.

Here the contrast is:

• the rabbit has long claws
• but it is very calm

That makes ale a natural choice.

You might also see a in other contrast sentences, but ale is stronger and fits better when the second part goes against what you might expect.

Yes. Polish word order is more flexible than English word order.

The sentence you have is neutral and natural:

• Królik też ma długie pazury, ale jest bardzo spokojny.

Other versions are possible, for example:

• Królik ma też długie pazury, ale jest bardzo spokojny.

The basic meaning stays the same, but the emphasis changes a little. Polish often uses word order to highlight information rather than to mark grammar.

Pazury means claws.

It is used especially for animals. For humans, the normal word for fingernails / nails is paznokcie.

So for a rabbit, pazury is the right word.

A few useful points:

• ó sounds like u
  • królik sounds roughly like KROO-leek
• ł sounds like English w
  • długie begins roughly dwoo-
• ż normally sounds like a hard zh, but at the end of a word it is devoiced
  • też sounds roughly like tesh

Very rough pronunciation guide:

• Królik = KROO-leek
• też = tesh
• długie = DWOO-gye
• pazury = pa-ZOO-ri
• spokojny = spo-KOY-ni

These are only approximations, but they help a lot at the beginning.

Bardzo means very.

It strengthens the adjective:

• spokojny = calm
• bardzo spokojny = very calm

In Polish, bardzo usually comes before the adjective or adverb it modifies, just like very in English.