Kad sam tužna, moja sestra je uvijek uz mene.

Because tužan/tužna changes for gender.

• tužan = masculine singular
• tužna = feminine singular

So this sentence is spoken by a woman or girl. If a man were speaking, it would be:

Kad sam tužan, moja sestra je uvijek uz mene.

Croatian often drops subject pronouns when they are already clear from the verb form.

Here, sam already tells you the subject is I. So ja is not necessary.

• Kad sam tužna = natural
• Kad ja sam tužna = not natural in standard Croatian

You can add ja only for emphasis, but normally Croatian leaves it out.

Yes. Kad and kada both mean when.

• kad is very common in everyday speech
• kada is slightly fuller or more formal in tone

So both are correct here:

• Kad sam tužna...
• Kada sam tužna...

The first one sounds very natural and conversational.

Because Kad sam tužna is a subordinate clause placed before the main clause.

Croatian normally separates that opening clause with a comma:

Kad sam tužna, moja sestra je uvijek uz mene.

This is similar to English punctuation in a sentence like When I'm sad, my sister is always by my side.

Sam and je are short unstressed forms of the verb biti (to be). These short forms are clitics, and Croatian usually places clitics near the beginning of their clause, in the usual second-position area.

So:

• Kad sam tužna is the normal order
• moja sestra je uvijek uz mene is also normal

That is why you do not usually say the more awkward neutral versions:

• Kad tužna sam
• moja sestra uvijek je uz mene

Croatian word order is flexible, but the position of short forms like sam and je follows special rules.

Not always, but it is perfectly natural here.

Moja sestra means my sister, and moja agrees with sestra:

• moja = feminine singular
• sestra = feminine singular

In context, Croatian can sometimes leave possession unstated if it is obvious, but using moja is clear and natural. It makes the relationship explicit.

Because the preposition uz requires the accusative case, and the accusative form of ja is mene.

So:

• ja = I
• mene = me

After uz, you use:

• uz mene = by me / beside me
• uz tebe = by you
• uz njega = by him

This is a case issue: prepositions in Croatian determine which form of the noun or pronoun must follow.

Literally, uz mene means beside me / by me.

But in this sentence it is also emotional, not just physical. It means something like:

• she is there for me
• she stands by me
• she supports me

So uz can express physical closeness, but also emotional support.

Because the meaning is slightly different.

• sa mnom = with me
• uz mene = by my side / there for me

In this sentence, uz mene is better because it suggests support, loyalty, and closeness when the speaker is sad.

Compare:

• Sestra je sa mnom. = My sister is with me.
• Sestra je uz mene. = My sister is by my side / supporting me.

So uz mene is the more expressive and idiomatic choice here.

Yes. Croatian word order is flexible, and uvijek (always) can move, but the emphasis changes.

The given sentence:

Moja sestra je uvijek uz mene.

is a neutral, natural way to say it.

You may also hear other orders, such as:

Uvijek je moja sestra uz mene.

This puts more emphasis on uvijek.

So the meaning stays close, but the rhythm and focus change. The original version is a very normal default choice.