Du kan regne med mig, hvis du har flere spørgsmål.

In this sentence, regne med is an idiomatic expression meaning count on, rely on, or depend on someone.

So:

• regne by itself can mean calculate
• but regne med often means count on / rely on

That is why Du kan regne med mig means You can count on me.

Examples:

• Jeg regner med dig. = I’m counting on you.
• Kan jeg regne med ham? = Can I rely on him?

So yes, the literal idea comes from counting, but in this sentence it is clearly the idiomatic meaning.

Because after the preposition med (with), Danish uses the object pronoun, not the subject pronoun.

Compare:

• jeg = I (subject form)
• mig = me (object form)

So:

• Du kan regne med mig = You can count on me not
• Du kan regne med jeg ❌

This works the same way as in English:

• with me ✅
• with I ❌

Other Danish examples:

• til mig = to me
• for ham = for him
• med os = with us

Here kan means something like can in English, but in this sentence it is best understood as expressing possibility / assurance:

• Du kan regne med mig = You can count on me

It does not really mean you have permission to count on me. It means I am reliable; it is safe for you to rely on me.

So the feeling is closer to:

• You can rely on me
• You can count on me
• I’ll be there for you

Hvis means if.

So:

• hvis du har flere spørgsmål = if you have more questions

It introduces a condition:

• You can count on me, if you have more questions

This is a very common Danish conjunction.

Examples:

• Hvis det regner, bliver vi hjemme. = If it rains, we’ll stay home.
• Ring til mig, hvis du har brug for hjælp. = Call me if you need help.

Because after hvis (if), Danish normally uses subordinate clause word order, where the subject comes before the finite verb.

So:

• hvis du har flere spørgsmål = if you have more questions

Structure:

• hvis = conjunction
• du = subject
• har = verb
• flere spørgsmål = object

This is normal for subordinate clauses in Danish.

Compare:

Main clause:

• Du har flere spørgsmål. = You have more questions.

Subordinate clause:

• ... hvis du har flere spørgsmål. = ... if you have more questions.

Flere means more when talking about countable things.

Since spørgsmål (questions) is countable, Danish uses flere:

• flere spørgsmål = more questions

By contrast, mere is used more often with uncountable things or in a more general sense:

• mere tid = more time
• mere kaffe = more coffee

So:

• flere spørgsmål ✅
• mere spørgsmål is generally not the normal choice here

A simple rule:

• flere = more of things you can count
• mere = more of something uncountable or abstract

Here spørgsmål is plural.

That can be confusing, because in Danish some nouns have the same form in the singular and plural.

For et spørgsmål:

• singular indefinite: et spørgsmål = a question
• singular definite: spørgsmålet = the question
• plural indefinite: spørgsmål = questions
• plural definite: spørgsmålene = the questions

In this sentence, flere makes it clear that it is plural:

• flere spørgsmål = more questions

Yes, Du kan stole på mig is possible, and it means You can trust me.

But there is a small difference:

• regne med nogen = count on / rely on someone
• stole på nogen = trust someone

In many situations they overlap, but the emphasis is slightly different:

• Du kan regne med mig suggests I’ll support you / I’ll be there / you can rely on me
• Du kan stole på mig suggests I am trustworthy / you can trust what I say or do

In your sentence, regne med mig sounds especially natural because it fits the supportive context of helping with more questions.

Yes. You can also say:

• Hvis du har flere spørgsmål, kan du regne med mig.

That is grammatically correct, but it sounds a little less natural in English translation as If you have more questions, you can count on me unless the speaker really wants to emphasize the condition first.

Notice what happens in the main clause after the hvis-clause comes first:

• Hvis du har flere spørgsmål, kan du regne med mig. not
• Hvis du har flere spørgsmål, du kan regne med mig. ❌

This is because Danish main clauses normally follow the verb-second rule, so kan comes before du after the fronted clause.

It is neutral and natural, but because it uses du, it is the normal informal/neutral second person singular form used in modern Danish.

That said, modern Danish uses du in most situations, even many polite ones. So this sentence works well in:

• everyday conversation
• emails
• messages
• teacher/student contexts
• customer support contexts, depending on tone

It sounds friendly and helpful rather than especially formal.

A careful pronunciation would be roughly:

• Du kan regne med mig, hvis du har flere spørgsmål.

Very approximate English-style guide:

• doo kan RINE-uh meth my, vis doo har FLAIR-uh SPER-smawl

A few important points:

• regne is often pronounced something like raine / rɑjnə rather than fully sounding every letter
• med often sounds softer than learners expect
• mig in modern standard Danish is often pronounced more like maj
• spørgsmål is tricky; the ø sound does not exist in English, and the word is often pronounced in a reduced way in normal speech

As usual in Danish, connected speech is often much less clear than the spelling suggests.

Yes, very natural. It sounds supportive, warm, and helpful.

Typical situations:

• a teacher to a student
• a tutor to a learner
• customer support
• a colleague helping someone
• a friend offering help

It gives the feeling:

• Feel free to come back to me
• I’m available if you need more help

If you want a slightly more standard service-style version, you might also hear:

• Du er velkommen til at spørge igen, hvis du har flere spørgsmål.
• Du kan altid kontakte mig, hvis du har flere spørgsmål.

But your original sentence is completely natural.