situmon ga mou hitotu arimasu.

が marks 質問 as the thing that exists in the sentence.

Because the verb is あります (to exist / there is for non-living things), the pattern is often:

[thing] が あります

So 質問があります literally follows the structure A question exists.

In natural English, that becomes something like I have a question or There is a question depending on context.

Japanese uses:

• あります for non-living things
• います for people and animals

A 質問 (question) is not a living thing, so あります is correct.

Compare:

• 質問があります。 = There is a question / I have a question.
• 先生がいます。 = The teacher is here / there is a teacher.

Here, もう means another, one more, or an additional.

So:

• 一つあります = there is one
• もう一つあります = there is one more

It adds the idea that this is not the first one. The speaker already asked something before and has an additional question.

一つ is the native Japanese counter meaning one thing. It belongs to the general 〜つ counting system:

• 一つ = one
• 二つ = two
• 三つ = three

This counter is often used when counting things in a general, non-technical way.

In 質問がもう一つあります, 一つ counts the number of questions: one more question.

Even though questions can sometimes be counted in other ways depending on context, 一つ is very common and natural here.

Both are possible.

• 質問がもう一つあります
• もう一つ質問があります

Both mean essentially the same thing: I have one more question.

The difference is mostly about focus and flow:

• 質問がもう一つあります starts by introducing question as the thing being talked about.
• もう一つ質問があります puts one more earlier, so the idea of an additional one is highlighted sooner.

In everyday conversation, もう一つ質問があります is especially common.

It is read:

しつもん が もう ひとつ あります。

A few notes:

• 質問 = しつもん
• 一つ = ひとつ
• あります = あります

So the full reading is:

しつもん が もう ひとつ あります。

Yes. 一つ and ひとつ are both used.

• 一つ uses kanji
• ひとつ uses hiragana

They mean the same thing. In many textbooks and everyday writing, either form may appear depending on style, level, and readability.

So these are both fine:

• 質問がもう一つあります。
• 質問がもうひとつあります。

Yes, but it changes the nuance.

• 質問がもう一つあります。
  This presents a question as something that exists. It sounds very natural when you are raising a new question.

• 質問はもう一つあります。
  This sounds more contrastive or topic-based, like As for questions, there is one more. It can imply comparison with something else.

For a simple I have one more question, が is the most natural choice.

Literally, it is closer to A question exists or There is a question.

But in real usage, Japanese often leaves out the subject when it is obvious. So in conversation, 質問があります is very often understood as:

I have a question.

Likewise, 質問がもう一つあります is naturally understood as:

I have one more question.

So the literal structure and the natural English translation are not always identical.

Because Japanese very often omits information that is clear from context.

If you are the one speaking, and you say:

質問があります。

people naturally understand that you are the one who has the question.

So Japanese does not need to say 私は unless there is a reason to emphasize it, contrast it, or make it especially clear.

Yes, depending on context.

For everyday speech, 一つ is very natural and common.

But in some situations, other counters may appear:

• 一問 often refers to one question on a test, quiz, or worksheet
• 一件 may be used for an inquiry or matter, especially in business contexts

Examples:

• テストの質問が一問あります。 = There is one test question.
• お問い合わせが一件あります。 = There is one inquiry.

For normal conversation like I have one more question, もう一つ質問があります is one of the most natural ways to say it.