Minulla on vielä yksi kysymys mielessä.

Because Finnish usually expresses having with a structure that literally looks more like on me / at me is ....

So:

• minä = I
• minulla = on me / at my place

In Finnish, Minulla on... means I have...

So:

• Minulla on yksi kysymys = I have one question

This is one of the most important basic Finnish patterns.

Because the verb agrees with the thing that exists, not with the possessor.

In Minulla on vielä yksi kysymys mielessä, the grammatical subject is really yksi kysymys (one question), which is third person singular, so the verb is:

• on = is

Literally, the structure is closer to:

• On me is still one question in mind

That is why you do not say Minulla olen...

Minulla is in the adessive case.

The adessive ending is:

• -lla / -llä

Here:

• minä → minulla

The adessive often means things like:

• on
• at
• by

In possession sentences, Finnish uses this case for the possessor:

• Minulla on auto = I have a car
• literally: At me / on me is a car

So minulla marks the person who has the question.

Because in this kind of possession sentence, the thing possessed is not treated like a normal direct object.

In English, we think:

• I have a question

and a question feels like an object.

But in Finnish, the structure is more like an existential sentence:

• Minulla on yksi kysymys
• literally: With me there is one question

So yksi kysymys stays in the nominative.

This is why you get:

• Minulla on kirja
• Minulla on idea
• Minulla on yksi kysymys

not object forms like kysymyksen here.

Here vielä means something like:

• still
• yet
• one more

In this sentence, it gives the idea that there remains an additional question.

So depending on context, the feeling can be:

• I still have one question in mind
• I have one more question in mind

Finnish vielä is very common and flexible, so its best English translation depends on context.

Yes. Finnish has no articles like a, an, or the.

So:

• Minulla on kysymys = I have a question
• Minulla on yksi kysymys = I have one question / one single question

Adding yksi makes the number more explicit. It can mean:

• literally one
• or emphatically one more / one specific remaining question

So in this sentence, yksi is not just functioning like English a. It really highlights the number one.

Mielessä is the inessive form of mieli, which can mean things like:

• mind
• thought
• mental state

The ending -ssa / -ssä means in.

So:

• mieli = mind
• mielessä = in mind / in the mind

In this sentence, mielessä means something like:

• in mind
• on my mind
• in my thoughts

So yksi kysymys mielessä means one question in mind.

It could.

Both are possible, depending on style and emphasis.

• mielessä = in mind / in the mind
• mielessäni = in my mind

In this sentence, minulla already makes it clear that the speaker is the one involved, so the possessive ending is not necessary.

Compare:

• Minulla on vielä yksi kysymys mielessä.
• Minulla on vielä yksi kysymys mielessäni.

The second is a bit more explicit and a little heavier. The first sounds very natural and idiomatic.

No, it is an idiomatic mental-expression use.

Finnish often uses location cases for abstract ideas too. So mielessä does not mean a physical place; it means something like:

• in mind
• in one’s thoughts
• on one’s mind

This is very normal in Finnish.

Finnish word order is flexible, but this order is natural and neutral.

A rough breakdown is:

• Minulla on = I have
• vielä = still / one more
• yksi kysymys = one question
• mielessä = in mind

Placing vielä before yksi kysymys makes it modify the idea of the remaining question naturally.

Other word orders are possible, but they change emphasis. For example:

• Yksi kysymys on vielä mielessäni
  = puts more focus on one question

The original sentence is a very normal default way to say it.

Yes.

• Minulla on vielä yksi kysymys = I still have one question
• Minulla on vielä yksi kysymys mielessä = I still have one question in mind

Adding mielessä emphasizes that the question is something you are still thinking about, not just something you technically possess as part of a conversation.

So mielessä adds a mental nuance: the question is still present in your thoughts.

Yes, it sounds natural.

It is a normal way to say that you still have one more question you want to ask or that one question remains in your mind.

Very common alternatives would also be:

• Minulla on vielä yksi kysymys.
• Mielessäni on vielä yksi kysymys.
• Vielä yksi kysymys on mielessäni.

But your original sentence is completely idiomatic.

In casual spoken Finnish, it might become something like:

• Mulla on vielä yks kysymys mielessä.

Changes:

• minulla → mulla
• yksi → yks

This is very common in speech, while the original sentence is standard written Finnish.