A barátnőm nem cukorral issza a teát, hanem mézzel.

It can mean either my girlfriend or my female friend. Hungarian does not always distinguish those two clearly in the noun itself.

• barát = friend / boyfriend
• barátnő = female friend / girlfriend
• barátnőm = my female friend / girlfriend

The ending -m means my.

So the exact meaning depends on context.

In Hungarian, possession is often shown by an ending on the noun rather than by a separate word like my.

So:

• barátnő = female friend / girlfriend
• barátnőm = my female friend / girlfriend

The -m is the 1st person singular possessive ending.

This is very common in Hungarian:

• könyv = book
• könyvem = my book

Hungarian often uses the definite article before a possessed noun when the noun is specific.

So:

• barátnőm = my girlfriend / my female friend
• a barátnőm = my girlfriend / my female friend, as a definite, identifiable person in the sentence

This is normal Hungarian usage. English does not do this, but Hungarian often does:

• A testvérem itt van. = My sibling is here.
• A barátnőm teát iszik. = My girlfriend/female friend is drinking tea.

Because teát is the accusative form. It marks the direct object of the verb.

• tea = tea
• teát = tea, as the thing being drunk

Since the sentence is about drinking tea, tea is the object, so Hungarian adds -t:

• issza a teát = drinks the tea

This is one of the most basic Hungarian case endings.

Because Hungarian has two kinds of verb conjugation here: indefinite and definite.

• iszik is the dictionary form, and it is used when there is no definite object
• issza is used when the object is definite

In this sentence, the object is definite:

• a teát = the tea

So Hungarian uses the definite conjugation:

• issza a teát

Compare:

• Teát iszik. = He/she drinks tea.
• A teát issza. = He/she drinks the tea.

They are in the instrumental-comitative case, which often means with.

So:

• cukor = sugar
• cukorral = with sugar
• méz = honey
• mézzel = with honey

In this sentence, the idea is drinks tea with sugar / with honey.

The basic ending is -val / -vel, but it often changes shape because of assimilation.

Because the ending is historically -val / -vel, but when it is added to a noun ending in a consonant, the v usually assimilates to that consonant.

So:

• cukor + val → cukorral

The v changes and the final consonant is doubled in spelling.

Other examples:

• bor
  • -val → borral = with wine
• kéz
  • -vel → kézzel = with a hand
• méz
  • -vel → mézzel = with honey

For the same reason as cukorral: assimilation.

The basic ending is -vel, but after méz, the v assimilates to the final consonant, so you get:

• méz + vel → mézzel

This is a very common spelling and pronunciation pattern in Hungarian.

nem ... hanem ... means not ..., but rather ... or not ..., but ... in a corrective contrast.

So here:

• nem cukorral = not with sugar
• hanem mézzel = but with honey

It is used when the second part corrects or replaces the first.

Compare:

• Nem Péter jött, hanem Anna. = It wasn’t Péter who came, but Anna.
• Nem kávét kér, hanem teát. = He/she doesn’t want coffee, but tea.

Because Hungarian word order is strongly connected to focus and contrast.

Here, cukorral is the contrasted element:

• not with sugar, but with honey

So Hungarian places the contrasted phrase before the verb:

• nem cukorral issza a teát, hanem mézzel

This word order highlights what is being corrected. In English, we do this mostly by stress; in Hungarian, word order helps do that job.

Yes, but the emphasis may change.

The given sentence is natural because it focuses on the contrast between sugar and honey.

For example:

• A barátnőm nem cukorral issza a teát, hanem mézzel.

This strongly highlights the with sugar / with honey contrast.

Hungarian allows some flexibility, but not every order sounds equally natural in every context. The version you were given is a very normal way to express this contrast.

Yes, literally it is the tea.

• a tea = the tea
• a teát = the tea (accusative)

Hungarian often uses the definite article in places where English might use either the or no article, depending on context. In this sentence, the tea is treated as a specific thing being drunk, so the definite article is natural.

It also triggers the definite verb form issza.

Yes. In natural English, you usually do not translate that initial a separately.

So:

• A barátnőm → my girlfriend / my female friend

Even though Hungarian uses the definite article, English normally does not say the my girlfriend. You simply translate it as my girlfriend.

It means she drinks tea with honey, not with sugar.

In natural English, that usually implies she sweetens it with honey. Hungarian expresses that with the instrumental form:

• cukorral = with sugar
• mézzel = with honey

So the idea is the same as She has/drinks her tea with honey rather than sugar.

Yes, it is natural Hungarian.

This pattern is very common for food and drink preferences:

• Kávét iszom tejjel. = I drink coffee with milk.
• A teát citrommal issza. = He/she drinks tea with lemon.
• Nem cukorral, hanem mézzel. = Not with sugar, but with honey.

So the sentence sounds normal and idiomatic.

Yes, but the effect is different.

• A barátnőm... is the more normal neutral form in a full sentence.
• Barátnőm... without the article can sound more literary, more compressed, or dependent on context.

In everyday standard Hungarian, A barátnőm nem cukorral issza a teát, hanem mézzel is the most natural choice.

They are:

• barátnő = female friend / girlfriend
• inni / iszik = to drink / drinks
• tea = tea
• cukor = sugar
• méz = honey
• nem = not
• hanem = but rather / but

And in the sentence they appear in changed forms:

• barátnőm = my female friend / girlfriend
• issza = drinks it / drinks the definite object
• teát = tea (accusative)
• cukorral = with sugar
• mézzel = with honey