Jeg har tillid til min søster, fordi hun altid siger sandheden.

Har tillid til is a fixed Danish expression. Literally, it is close to have trust/confidence in.

So the structure is:

• har = have
• tillid = trust / confidence
• til = to / in, as required by the expression

English often uses one verb, trust, where Danish uses a verb + noun + preposition phrase instead.

So jeg har tillid til min søster is a very normal way to say I trust my sister.

Because tillid normally goes with the preposition til when you say who or what the trust is directed toward.

The full pattern is:

• have tillid til nogen
• have tillid til noget

Examples:

• Jeg har tillid til ham.
• Vi har tillid til systemet.

This is something you should learn as a chunk: have tillid til.
Even if English uses trust someone without a preposition, Danish needs til here.

Yes. Jeg stoler på min søster is also correct and natural.

The two expressions are close in meaning:

• have tillid til = have trust/confidence in
• stole på = trust / rely on

In many everyday situations, they are interchangeable.
A small nuance is that have tillid til can sound a bit more like having confidence in someone’s character or honesty, while stole på often feels a bit more everyday and can also suggest relying on someone.

So in this sentence, both work well.

Because Danish possessive words change according to the gender and number of the noun being possessed.

Here, søster is:

• singular
• common gender

So the correct form is min:

• min søster

Compare:

• min søster = my sister
• mit hus = my house
• mine søstre = my sisters

A useful mini-pattern:

• min
  • singular common gender
• mit
  • singular neuter
• mine
  • plural

Because when Danish uses a possessive like min, din, hans, vores, etc. before the noun, the noun normally stays in its indefinite form.

So you say:

• min søster
• hans bil
• vores hus

not:

• min søsteren
• hans bilen
• vores huset

The possessive already makes the noun definite in meaning, so Danish does not usually add the definite ending too.

There is also a spoken/colloquial pattern like søsteren min, but the normal neutral form to learn first is min søster.

Because hun is the subject form of she, while hende is the object form of her.

In fordi hun altid siger sandheden, the sister is the one doing the action of saying, so Danish uses the subject pronoun:

• hun siger = she says

Compare:

• Jeg kender hende. = I know her.
• Jeg taler med hende. = I speak with her.

So:

• hun = subject
• hende = object

Because fordi introduces a subordinate clause, and Danish word order changes in subordinate clauses.

In a normal main clause, Danish follows the V2 rule: the finite verb comes in second position.

Example:

• Hun siger altid sandheden.

But after fordi, the clause is subordinate, and the word order is typically:

• fordi + subject + adverb + finite verb

So:

• fordi hun altid siger sandheden

This is why fordi siger hun... is not correct here.

This is one of the big word-order differences between main clauses and subordinate clauses in Danish.

In a main clause:

• Hun siger altid sandheden.

Here the finite verb siger comes early because of the V2 rule, and altid comes after it.

In a subordinate clause after fordi:

• fordi hun altid siger sandheden

Now the adverb altid comes before the finite verb.

So the contrast is:

• Hun siger altid sandheden.
• ... fordi hun altid siger sandheden.

That pattern is very important in Danish grammar.

Because the normal expression is sige sandheden, which corresponds to English tell the truth.

So Danish usually uses the definite form here:

• sandheden = the truth

This is idiomatic. It is the standard way to express the idea.

Just sandhed can exist in other contexts, especially in more abstract or philosophical language, but in this sentence the natural phrase is:

• sige sandheden

Because sige sandheden is the usual everyday Danish idiom for tell the truth.

Even though English uses tell, Danish most often uses say here:

• sige sandheden

Fortælle sandheden is understandable and can be used, but it may sound a bit more marked, as if someone is revealing or recounting the truth in a fuller sense.

For the simple idea of being honest, sige sandheden is the most natural choice.

Because the sentence describes:

• a present state: jeg har tillid
• a habitual action: hun altid siger sandheden

Danish uses the present tense for both of these, just as English often does.

So:

• har = have / have got
• siger = says

There is no special separate verb form here for habitual meaning.
The word altid already shows that this is something she does regularly.

Because fordi introduces a subordinate clause, and many Danish writers place a comma before such clauses.

So this punctuation is very normal:

• Jeg har tillid til min søster, fordi hun altid siger sandheden.

You may also see Danish written without that comma, depending on comma style:

• Jeg har tillid til min søster fordi hun altid siger sandheden.

So the comma before fordi is common and correct in many contexts, but Danish punctuation conventions allow some variation here.