Kad je pločnik klizav, moja sestra hoda sporije da ne bi ozlijedila gležanj.

Here kad means when or whenever.

In this sentence, Kad je pločnik klizav means When/Whenever the sidewalk is slippery.

Kad and kada usually mean the same thing. The difference is mostly style:

• kad = shorter, very common in everyday speech
• kada = a bit more formal or more emphatic in some contexts

So here, kad is completely natural.

Je is the 3rd person singular present tense of biti (to be).

Croatian often uses to be to link a subject with an adjective, just like English:

• Pločnik je klizav = The sidewalk is slippery

So:

• pločnik = the sidewalk
• je = is
• klizav = slippery

Because pločnik is the subject of the clause, it is in the nominative singular.

Klizav is an adjective, and it must agree with pločnik in:

• gender
• number
• case

Since pločnik is:

• masculine
• singular
• nominative

the adjective also appears as:

• klizav

If the noun changed, the adjective would change too. For example:

• cesta je klizava = the road is slippery
  because cesta is feminine

Because hodati specifically means to walk, while ići means to go.

So:

• hoda = walks
• ide = goes

In this sentence, the speaker is talking about the way the sister moves on a slippery sidewalk, so hoda is the more precise choice.

Compare:

• Moja sestra hoda sporije. = My sister walks more slowly.
• Moja sestra ide kući. = My sister is going home.

Sporije means more slowly.

It is the comparative form of the adverb sporo (slowly):

• sporo = slowly
• sporije = more slowly

This is an adverb, because it describes how she walks.

A common point of confusion is the difference between the adjective and adverb:

• spor / sporiji = slow / slower
• sporo / sporije = slowly / more slowly

So in this sentence:

• hoda sporije = walks more slowly

Yes. Croatian often omits possessives when they are obvious from context.

So both of these are possible:

• Moja sestra hoda sporije...
• Sestra hoda sporije...

Including moja makes it explicit: my sister.

Croatian sometimes uses possessives less often than English does, especially when the relationship is already clear.

This is a very common Croatian way to express purpose, especially negative purpose.

Here it means:

• so that she wouldn’t injure
• so as not to injure
• in order not to injure

So:

• da introduces the purpose clause
• ne makes it negative
• bi ozlijedila gives the sense of a possible unwanted result

Whole phrase:

• da ne bi ozlijedila gležanj = so that she wouldn’t injure her ankle

Not by itself in the meaning of the sentence.

It may look like a past form, because ozlijedila is the l-participle form used in the past and conditional. But here it is used with bi, so together they form a conditional-type construction, not a plain past tense.

Compare:

• Ozlijedila je gležanj. = She injured her ankle.
  This is past tense.
• Da ne bi ozlijedila gležanj. = So that she wouldn’t injure her ankle.
  This is not past tense here.

So the important thing is that bi + ozlijedila works as one unit.

Because it agrees with the implied subject, which is moja sestra.

The subject is feminine singular, so the participle is also feminine singular:

• sestra ... ozlijedila

If the subject were masculine, you would get:

• brat ... ozlijedio

This agreement is very common in Croatian with past and conditional-type forms.

Because bi is a clitic-like auxiliary, and in this kind of clause the normal order is:

• da + ne + bi + participle

So:

• da ne bi ozlijedila

This is the standard and natural order.

For learners, it is best to remember the whole pattern as a chunk:

• da ne bi + l-participle

It is a very common structure for so that ... wouldn’t / so as not to ...

Because gležanj is the direct object of ozlijediti (to injure), so it is in the accusative singular.

For masculine inanimate nouns, the accusative singular is often the same as the nominative singular.

So:

• nominative: gležanj
• accusative: gležanj

That is why the form does not change visibly here.

Yes. Ozlijediti is a perfective verb, and it fits well here because the sentence refers to a possible single event: injuring the ankle.

Croatian often uses a perfective verb when talking about:

• one complete action
• a possible result
• a specific event to be avoided

So da ne bi ozlijedila gležanj naturally means avoiding one possible injury event.

Not completely. Croatian word order is fairly flexible, but some parts are more natural than others.

This sentence starts with the condition:

• Kad je pločnik klizav, ...

That is very natural, because it sets up the situation first.

Also, small words like je and bi tend to appear in specific positions:

• Kad je pločnik klizav
• da ne bi ozlijedila

So while Croatian allows some movement, you cannot rearrange everything freely without sounding unnatural.

There is a comma after klizav because Kad je pločnik klizav is an introductory subordinate clause.

So the structure is:

• Kad je pločnik klizav, = introductory clause
• moja sestra hoda sporije... = main clause

The final da-clause expresses purpose and is very tightly connected to the verb phrase hoda sporije, so it is often written without a comma:

• hoda sporije da ne bi ozlijedila gležanj

That is normal and natural in Croatian.