Η κόρη της θέλει μεγαλύτερο ενυδρείο, αλλά ο πατέρας της λέει ότι το μικρό είναι αρκετό για τώρα.

That is the normal Greek pattern for possession with family members and many other nouns:

• η κόρη της = literally the daughter of her
• ο πατέρας της = literally the father of her

So Greek usually keeps the definite article and then adds the possessive pronoun after the noun. English drops the in this kind of phrase, but Greek normally does not.

Because της here is a weak possessive form, historically a genitive pronoun, and in Modern Greek it normally comes after the noun:

• η κόρη της = her daughter
• ο πατέρας της = her father

This is one of the most basic word-order differences from English. Greek does not usually put a simple possessive equivalent of her directly before the noun the way English does.

Not necessarily. It most naturally refers to the same female person both times:

• Η κόρη της = Her daughter
• ο πατέρας της = her father

So the sentence is talking about one female person, and then mentioning both her daughter and her father. Greek repeats the possessive pronoun where English would also repeat her if both relationships are stated.

Because μεγαλύτερο agrees with ενυδρείο, and ενυδρείο is a neuter noun.

• ο μεγαλύτερος = masculine
• η μεγαλύτερη = feminine
• το μεγαλύτερο = neuter

Here the phrase is:

• μεγαλύτερο ενυδρείο = a bigger aquarium

Since ενυδρείο is neuter singular, the adjective must also be neuter singular.

It is the comparative form of μεγάλος (big), so it means bigger or larger.

• μεγάλο ενυδρείο = a big aquarium
• μεγαλύτερο ενυδρείο = a bigger aquarium

A learner should also know that Greek often uses another comparative pattern:

• πιο μεγάλο = bigger

So μεγαλύτερο and πιο μεγάλο can often express the same idea.

Greek can omit the indefinite article in places where English normally uses a/an, especially when the object is nonspecific.

So:

• θέλει μεγαλύτερο ενυδρείο = she wants a bigger aquarium

You could also say:

• θέλει ένα μεγαλύτερο ενυδρείο

That also means she wants a bigger aquarium. In this sentence, leaving out ένα sounds perfectly natural.

It is in the accusative case because it is the direct object of θέλει (wants).

• θέλει τι; = wants what?
• μεγαλύτερο ενυδρείο

Since ενυδρείο is neuter singular, its nominative and accusative forms look the same, so you do not see a change in the ending here. But functionally, it is accusative.

Because Greek can use article + adjective by itself when the noun is understood from context.

Here, το μικρό stands for:

• το μικρό ενυδρείο = the small aquarium

In English, we often translate that as the small one to sound natural. Greek does this kind of omission very often when the noun is obvious.

Because αρκετό is a predicate adjective agreeing with το μικρό, which stands for το μικρό ενυδρείο.

Since the understood noun is neuter singular, the adjective is also neuter singular:

• το μικρό είναι αρκετό = the small one is enough

If the noun were feminine or masculine, the form of αρκετός would change accordingly.

Ότι introduces a content clause, like English that after a verb such as say:

• λέει ότι... = says that...

So:

• ο πατέρας της λέει ότι το μικρό είναι αρκετό
  = her father says that the small one is enough

In English, that is often optional. In Greek, using ότι is very normal here.

Για τώρα means for now, for the time being, or at least at the moment.

So:

• είναι αρκετό για τώρα = it is enough for now

This suggests the situation may change later. The father is not necessarily saying never; he is saying the current small aquarium is sufficient at the moment.

It can be either, depending on context. Greek present tense often covers both a general present and a current ongoing present.

So λέει can mean:

• says
• is saying

In this sentence, English usually prefers says:

• her father says that the small one is enough for now

But the Greek form itself does not force only one of those English choices.