Donald Trump held his first press conference as US President-elect at Trump Tower in New York early this morning (AEDT).

As expected, he was asked about reports that exploded across the internet on Wednesday regarding unsubstantiated claims that Russia has compromising personal and financial information about the President-elect — reports that Mr Trump labelled as "fake news" during the conference.

But journalists were also looking for more information on his policies on tax, trade and international relations, and his ties to business interests around the world.

We asked ABC journalists and experts what they would have asked Mr Trump and why.

Since the election, many people have been watching for signs of presidential seriousness, yet you are still trading insults with comics and boasting about ratings. Will we see a different person after the inauguration?

Michael Carey, ABC International Editor

Many Americans worry whether Mr Trump has the temperament for this high office, which requires careful judgement and an ability to focus on the details of the many important issues he will face.

Tweeting about Saturday Night Live or the poor audience for Arnold Schwarzenegger's The Celebrity Apprentice does not fill them with confidence.

Does he have the ability to grow a thicker skin and rise to the position? Will he — can he — be presidential?

Given the tensions in Ukraine and fears in the Baltic states about Russia, what would you tell the leaders of countries who fear Russia's resurgent military, and are concerned the US may not live up to its NATO commitments to protect them?

Norman Hermant, ABC social affairs correspondent and former Moscow correspondent

This question gets to the heart of concerns over the election hacking story.

If the allegations (which are mounting daily) are backed up, it would mean the Kremlin did in fact actively interfere to produce a Trump victory.

The reason for that — Moscow believes it would a have a freer hand with Mr Trump in the White House. The answer to this question could tell much about which way Mr Trump wants this played out in the media.

If he deflects, and repeats the line that the priority for the US is now concerted action with Russia against militant Islam, then countries like Estonia and Ukraine have reason to be worried.

I suspect the President-elect might seek to turn the tables on Moscow and flip the script, essentially warning Moscow against further intimidation of its neighbours.

But that would be a very public retreat from previous indications of warming relations with Russia after January 20.

You have said you still plan to ban Muslims from entering the US and to build a Muslim "registry". How would the registry work? What evidence is there that a ban would work to reduce terrorism?

Patricia Karvelas, presenter RN Drive

Why would I ask this? The President-elect has had a confusing position on this pledge.

He at one point clarified the policy to only suspend immigration from countries that have been hot beds of terrorism.

The policy and how it would be implemented needs immediate clarification.

Aren't your plans to stimulate the economy at this stage of the cycle dangerous and counterproductive?

Phillip Lasker, ABC finance correspondent

Some argue the US economic recovery is already progressing at a sustainable pace and unemployment is falling to acceptable levels.

Mr Trump's nominee for Treasury Secretary, Steve Mnuchin, wants to accelerate US growth to 3-4 per cent.

The US Fed would find this unacceptable without much higher interest rates to combat inflation.

The US dollar is already strengthening (particularly against the Mexican peso) making the US even less competitive due to the improvement in economic growth and Trumps stimulus plans.

Inflation expectations and interest rates have also gone up and may have to rise more quickly than initially anticipated. Also the planned massive tax cuts would put pressure on US debt.

Where are you going to go on your first foreign trip?

Dr Gorana Grgic, lecturer in US Politics and Foreign Policy at the United States Studies Centre

Is he going to do that same old thing and just go to Europe and say the Trans-Atlantic links are the core of the United States foreign policy... since World War II? Or is he going to break from that tradition?

Is he going to go to Asia? Maybe. And if so, where?

It would be really interesting to see what he does and says to that effect because there is a lot of symbolism around it.

Why do you argue that better relations with Russia are in America's interest, but that a more robust American position is required on China?

Hamish Macdonald, presenter RN Summer Breakfast

There is some logic behind Mr Trump's argument that it is in America's interest and in the world's interest that Russia and America have a better relationship.

Not everyone would agree with that, but he is not alone in making that case.

However, this raises a further question: why then would it not be in both America and the world's interest that China and America have a better relationship, too?

President-elect Trump, on the one hand, appears hell-bent on a trade war with China, at the very least, whilst on the other hand appears willing to forgive all manner of misdeeds on Russia's part; Syria and Crimea to name two.