Este használom a mosogatógépet, hogy reggel tiszták legyenek a csészék.

Because a mosogatógépet is a definite object: it means the dishwasher, not a dishwasher.

Hungarian verbs often have two conjugations:

• indefinite conjugation: used when there is no definite object, or the object is indefinite
• definite conjugation: used when the object is definite/specific

So:

• használok = I use / I am using with no definite object
• használom = I use it / I use the specific one

In this sentence, a mosogatógépet is specific, so használom is the correct form.

The -t is the accusative ending, which marks the direct object of the verb.

Here:

• mosogatógép = dishwasher
• mosogatógépet = dishwasher as the thing being used

Since I use the dishwasher, the dishwasher is the object, so Hungarian marks it with -t.

Este means in the evening / tonight, depending on context.

Hungarian often uses simple time words without a separate word for in the:

• reggel = in the morning
• este = in the evening
• éjjel = at night

So Hungarian does not need to say something like in the evening word-for-word. The single word este already does that job.

Hogy introduces a subordinate clause. In this sentence, it means something like:

• so that
• in order that

So the structure is:

• Este használom a mosogatógépet = I use the dishwasher in the evening
• hogy reggel tiszták legyenek a csészék = so that the cups are clean in the morning

It expresses purpose.

Because after hogy in a purpose clause, Hungarian commonly uses the imperative/subjunctive-type form.

So:

• lesznek = they will be / they are going to be
• legyenek = that they be / so that they be

In natural English, we usually translate legyenek here as are or will be, but the Hungarian grammar is different.

Formally, legyenek is the 3rd person plural imperative form of lenni (to be), but in sentences like this it functions like a subjunctive:

• hogy ... legyenek = so that ... may be / will be

Because csészék is plural, and when an adjective is used as the predicate with to be, Hungarian usually makes the adjective plural too.

So:

• A csésze tiszta. = The cup is clean.
• A csészék tiszták. = The cups are clean.

That is why the sentence has:

• tiszták legyenek a csészék = the cups should be clean

A useful contrast:

• tiszta csészék = clean cups
  Here the adjective comes before the noun, and it does not take a plural ending.
• a csészék tiszták = the cups are clean
  Here the adjective is a predicate, so it does take plural -k.

Because a csészék is the subject of the subordinate clause, not the object.

In:

• hogy reggel tiszták legyenek a csészék

the cups are the things that are clean, so they are the subject:

• the cups are clean

If it were csészéket, that would be accusative, meaning the cups were the direct object of some verb.

So:

• a csészék = the cups
• a csészéket = the cups (as object)

Yes, Hungarian word order is flexible, and it often reflects topic, focus, and emphasis, not just basic grammar.

This version highlights the intended result:

• reggel = in the morning
• tiszták = clean

So the sentence naturally emphasizes the goal: by morning, clean is the important idea.

Other word orders are possible, for example:

• hogy a csészék reggel tiszták legyenek
• hogy reggel a csészék tiszták legyenek

These are also grammatical, but they shift the emphasis slightly.

A good practical way to understand the given order is:

• the time reggel is set first
• the desired state tiszták is prominent
• a csészék comes later because they are already known from context

Because Hungarian verb endings usually already show the subject.

használom tells you that the subject is:

• first person singular = I

So én is not necessary.

You could say:

• Én este használom a mosogatógépet...

but that would add emphasis, something like:

• I use the dishwasher in the evening

Without special emphasis, Hungarian normally leaves the pronoun out.

By default, it sounds habitual or regular:

• I use the dishwasher in the evening so that the cups are clean in the morning.

That is because the present tense in Hungarian often describes:

• habits
• routines
• planned actions

Depending on context, it could also refer to a specific situation, especially in everyday speech. But if you see the sentence by itself, many learners will naturally understand it as a routine.

Yes, and the meaning would shift slightly.

• reggel = in the morning
• reggelre = by morning / for the morning

So:

• hogy reggel tiszták legyenek a csészék
  = so that the cups are clean in the morning

• hogy reggelre tiszták legyenek a csészék
  = so that the cups are clean by morning

The version with reggelre emphasizes the deadline/result by that time a bit more. Both can be natural, but they are not exactly identical.