Sú sem getur huggað hana best er systir hennar.

In this sentence, sú sem means the one who and refers to a female person.

• sú = feminine singular form of sá
• sem = relative particle, like who/that

So sú sem getur huggað hana best is literally something like the female one who can comfort her best.

Because sú is feminine singular.

Icelandic often matches this kind of pronoun to the gender of the person being referred to:

• sá sem = the one who (masculine)
• sú sem = the one who (feminine)
• það sem = that which / what (neuter, often for things or abstract reference)

Here the person is female, and the later phrase systir hennar also confirms that.

sem introduces a relative clause, so here it works like English who or that.

A useful thing to know is that sem is indeclinable:

• it does not change for gender
• it does not change for number
• it does not change for case

So Icelandic uses the same sem in many different situations where English might use who, whom, that, or which.

getur is the 3rd person singular present of geta, meaning can / be able to.

After geta, Icelandic normally uses the verb in the supine form (often called sagnbót), so:

• dictionary form: hugga
• after geta: huggað

So getur huggað is the normal Icelandic pattern for can comfort.

This is why you do not see getur hugga here.

Because hugga takes a direct object in the accusative case.

So:

• hana = accusative her
• henni = dative her

Since hana is the person being comforted, accusative is required.

Because Icelandic pronouns change form depending on case.

For hún (she), the main forms are:

• hún = nominative
• hana = accusative
• henni = dative
• hennar = genitive

In this sentence:

• hana is the direct object of huggað
• hennar shows possession in systir hennar

So English uses her for both, but Icelandic uses different forms.

Because best is an adverb, not an adjective.

It modifies the verb idea huggað:

• vel = well
• betur = better
• best = best

So hugga hana best means comfort her best.

If you were describing a noun with an adjective, then you would need an agreeing adjective form such as besta. But that is not what is happening here.

Because this is a sentence with vera (to be) identifying someone:

• Sú sem getur huggað hana best = the subject
• er systir hennar = what that subject is identified as

So systir hennar is the predicate complement after er.

This is a very common Icelandic pattern, just like English X is Y.

systir is in the nominative.

After vera in identity statements like this, the noun naming or identifying the person is normally nominative:

• Hún er kennari.
• Þetta er vinur minn.
• ... er systir hennar.

So even though it comes after the verb, it is not an object.

That is the normal neutral Icelandic order for this kind of phrase.

So Icelandic commonly says:

• bróðir minn = my brother
• systir hennar = her sister
• húsið okkar = our house

Putting the possessive after the noun is very natural in Icelandic. Other orders can occur for emphasis, but systir hennar is the standard choice here.

The whole phrase Sú sem getur huggað hana best is the subject.

Inside that subject:

• sú is the head word
• sem getur huggað hana best is a relative clause describing it

So the sentence structure is basically:

• [The one who can comfort her best] = subject
• [is her sister] = predicate

That is why the sentence means that the person fitting that description turns out to be her sister.

Yes. That would also be a natural Icelandic sentence.

The difference is mainly focus:

• Sú sem getur huggað hana best er systir hennar
  → focuses first on the one who can comfort her best

• Systir hennar er sú sem getur huggað hana best
  → focuses first on her sister

So the core meaning stays the same, but the information is presented differently.