Mám další otázku.

Czech changes the noun ending according to its grammatical case.

• The basic dictionary form is otázka (feminine, nominative singular).
• After mám (from mít, to have), the object must be in the accusative case.

For feminine nouns like otázka, nominative -a usually changes to accusative -u:

• otázka → otázku

So Mám otázku = I have a question (with otázku in the accusative).

Další can mean both “another” and “next”, depending on context.

• Mám další otázku. – I have another question.
• Další stanice je… – The next station is…

In Mám další otázku, it is understood as “another / an additional” question, not necessarily the next in a sequence, just one more.

In neutral Czech word order, adjectives normally come before the noun:

• další otázka – another question
• nový byt – a new flat
• velký pes – a big dog

Putting the adjective after the noun (e.g. otázku další) is possible only in special, marked styles (poetic, very emphatic, or archaic) and would sound strange in normal speech.

So the natural order is další otázku, not otázku další.

• Mám otázku. – I have a question. (no implication you asked anything before)
• Mám další otázku. – I have another question. / I have one more question. (implies you or someone already asked at least one question before)

So další adds the idea of “one more / an additional one”.

Yes, but there are small nuances:

• Mám další otázku. – I have another / an additional question.
• Mám jinou otázku. – I have a different question (not the same as before; stressing difference).
• Mám ještě jednu otázku. – I have one more question (literally “still one question”; emphasizes the number “one more”).

All are correct; in many contexts další and ještě jednu can both translate as another / one more.

You normally do not need the pronoun já in Czech, because the verb ending -m in mám already shows that the subject is “I”.

• Mám další otázku. – neutral, standard.
• Já mám další otázku. – adds emphasis to I, like “I have another question (as opposed to someone else).”

Use Já mám… when you want to stress who has the question; otherwise, just Mám další otázku is more natural.

The infinitive is mít – to have.

Present tense (singular + plural):

• já mám – I have
• ty máš – you have (singular, informal)

• on / ona / ono má – he / she / it has

• my máme – we have
• vy máte – you have (plural or formal)
• oni / ony / ona mají – they have

So Mám další otázku. = I have another question.

Using mít and adjusting the noun:

• Máme další otázku. – We have another question.
• Máme další otázky. – We have more / other questions.
• Mají další otázku. – They have another question.
• Mají další otázky. – They have more / other questions.

Notice the plural of otázka:

• nominative plural: otázky
• accusative plural: also otázky

So in Máme další otázky, otázky is accusative plural.

Yes, it is perfectly fine and natural in both informal and formal situations.

You might also hear slightly more formal or indirect options:

• Mám ještě jednu otázku. – I have one more question.
• Chtěl(a) bych se ještě na něco zeptat. – I would like to ask something else.
• Měl(a) bych ještě jednu otázku. – I would have one more question. (polite, conditional)

But Mám další otázku is already acceptable and polite in most contexts.

Rough guide with English-like approximations:

• Mám – like maam with a long a (hold the vowel longer).
• další – dal like dull but with a as in father, š like sh in she, í a long *ee sound → DAL-shee.
• otázku – o as in or, tá with a long a (like taa), z as in zoo, ku like koo → o-TAAZ-koo.

Stress in Czech is almost always on the first syllable of each word:

• MÁM DAL‑ší O‑táz‑ku (stress: bold capital syllables in this representation).

Yes, a small nuance:

• Mám další otázku. – I have another / one more question. (neutral, the usual way to say this)
• Mám otázku navíc. – I have an extra question. (literally “a question in addition”; can sound like it’s beyond what was expected or planned)

You’ll hear Mám další otázku far more often in ordinary conversation when you simply mean “I have another question.”