Αυτή κοστίζει λιγότερο από την άλλη.

Here Αυτή means this one.

Greek αυτός, αυτή, αυτό can be:

• a demonstrative: this
• a personal pronoun in some contexts: he / she / it

In this sentence, Αυτή κοστίζει..., it means this one costs..., not she costs.... The context is probably about objects, such as dresses, bags, or shirts.

Because the word it stands for is feminine.

Greek demonstratives change for gender:

• αυτός = masculine
• αυτή = feminine
• αυτό = neuter

So if the hidden noun is something feminine, such as:

• η φούστα = the skirt
• η μπλούζα = the blouse
• η τσάντα = the bag

then you use Αυτή.

Because Greek often omits a noun when it is obvious from context.

So:

• Αυτή = this one
• την άλλη = the other one

English does this too, but Greek does it very naturally. If two feminine items are being compared, the noun does not need to be repeated.

Κοστίζει is the 3rd person singular present tense of κοστίζω, meaning to cost.

So:

• κοστίζω = I cost / I am costing
• κοστίζει = it costs / she costs / this one costs

In this sentence, the subject is Αυτή, so κοστίζει means this one costs.

Because λιγότερο here is being used as an adverb, not an adjective.

It modifies the verb κοστίζει:

• κοστίζει λιγότερο = costs less

So it means less in the sense of to a lesser degree / amount.

If you were using λιγότερος, λιγότερη, λιγότερο as an adjective, it would agree with a noun. But here it does not describe the object directly; it describes the action of costing.

Από means than in this comparison.

Greek commonly forms comparisons like this:

• λιγότερο από... = less than...
• περισσότερο από... = more than...
• μεγαλύτερο από... = bigger than...

So:

• Αυτή κοστίζει λιγότερο από την άλλη
  = This one costs less than the other one

Although από often means from, in comparisons it works like than.

Την άλλη means the other one.

Breakdown:

• την = feminine singular accusative article
• άλλη = other in feminine singular accusative

Greek often uses the article with άλλος / άλλη / άλλο, so την άλλη is a very normal way to say the other one.

Because από takes the accusative in Modern Greek.

So after από, you get:

• από τον...
• από την...
• από το...

That is why the sentence has:

• από την άλλη

not a nominative form.

Because Αυτή is the subject of the sentence, so it is in the nominative case.

• αυτή = nominative feminine singular
• αυτήν = accusative feminine singular

In this sentence, this one is doing the action of costing, so nominative is required:

• Αυτή κοστίζει...

If it were an object, you might see αυτήν, though in everyday spelling and speech the final -ν is often dropped in some contexts.

Yes. That is also correct, but it is slightly different in structure.

• Αυτή κοστίζει λιγότερο από την άλλη = This one costs less than the other one
• Αυτή είναι φθηνότερη από την άλλη = This one is cheaper than the other one

The meaning is very close. The first sentence uses the verb to cost, while the second uses the adjective cheaper.

Not completely. Greek word order is more flexible than English.

The neutral, natural version is:

• Αυτή κοστίζει λιγότερο από την άλλη.

But Greek can move words around for emphasis. For example, you may hear variations depending on what the speaker wants to stress.

Still, for a learner, the given word order is the safest and most standard one to use.

Yes, very normal.

Some common patterns are:

• κοστίζει λιγότερο από... = costs less than...
• δουλεύει λιγότερο από... = works less than...
• τρώει λιγότερο από... = eats less than...

So λιγότερο από is a basic and useful pattern to remember.