Donald Trump has attempted to negotiate a potential TikTok sale on live television, in what was supposed to be an announcement about investment in artificial intelligence (AI) infrastructure.

The US president was holding a news conference about a $500bn (£405bn) investment in AI infrastructure in the country, but was questioned about a range of topics.

At one point he attempted to negotiate the sale of Tiktok with American businessman Larry Ellison, who is said to be worth more than $204bn (£165bn).

Mr Trump also had to defend some of his actions just one day into his second term.

When the topic of TikTok was raised, Mr Trump said he was “open” to his close friend Elon Musk buying the app, adding: “I would be, if he wanted to buy it. I’d like Larry [Ellison] to buy it too.”

He continued: “I have the right to make a deal, the deal I’m thinking about, Larry let’s negotiate in front of the media.

“The deal I think is this. I’ve met with the owners of TikTok, the big owners, it’s worthless if it doesn’t get a permit… with a permit it’s worth like a trillion dollars.

“What I’m thinking of saying to someone is buy it and give half to the US, half, and we’ll give you a permit… the US will be the ultimate partner and the US will make it very worthwhile for them.”

“Sounds like a good deal to me Mr President,” Mr Ellison said, when asked by the president about the offer.

During the press conference, Mr Trump also said he received a “very nice letter” from the outgoing Joe Biden.

“It was a little bit of an inspirational type letter, joy, do a good job, important, very important the job is, I think it was a nice letter, I think I should let people see it… I appreciated the letter,” he said.

Capitol riot pardons

As part of a blitz of executive orders Mr Trump signed on Monday, he issued pardons for more than 1,500 people involved in the Capitol riot – including the Proud Boys and Oath Keepers leaders.

When asked how he justified pardoning convicted violent rioters, some of whom attacked police, he said: “I am the friend of police more than any president that has been in this office.

“They’ve been given a pardon, I thought their sentences were ridiculous and excessive.”

When further questioned over the words of his vice president JD Vance, who said no violent rioters would be pardoned, Mr Trump claimed they had “served years in jail and murderers don’t even go to jail in this country”.

Tariff countdown

Across the campaign trail, Mr Trump has repeatedly raised the prospect of using tariffs against other countries.

But for the first time, he gave a date for potentially bringing them in.

He vowed to hit the European Union (EU) with tariffs and said his administration was discussing imposing an additional 10% tariff on goods imported from China from 1 February because, he claimed, fentanyl was being sent from China to Mexico and Canada, then on to the US.

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“The European Union is very, very bad to us, so they’re going to be in for tariffs. It’s the only way… you’re going to get fairness,” he said.

Donald Trump signed more than 100 executive orders on his inauguration day.

It has become standard practice for new presidents to use them within hours of taking office – Joe Biden signed 17 on his first day.

They are arguably the president’s most powerful tool for enacting change – as they have the same force behind them as legislation – and bypass both Houses of Congress.

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Mr Trump’s inauguration day executive orders included declaring a national emergency at the US-Mexico border, withdrawing US birthrights from migrants’ children, and taking the US out of both the Paris Climate Agreement and the World Health Organisation.

But they do have limits – and can be subject to legal challenges.

What are they – and how do they work?

Executive orders are official instructions from the president about how US federal agencies, such as government departments and the FBI, should use their resources.

They are enshrined in the second article of the constitution, which states: “The executive power shall be vested in a president of the United States of America.”

Effectively, they are a way for the president to dictate how the federal government should be run.

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They can take various forms – from laying out major policies and requesting official reports to giving federal employees days off for public holidays.

The president’s role as commander in chief means they can also be used to control what the military does.

How quickly do they take effect?

It depends on the subject matter – and the work required to achieve the president’s aims.

Executive orders that are relatively straight forward and face no opposition can be acted upon straight away.

For example, one of Mr Trump’s latest ones pardoned all of the 6 January rioters, declaring any still behind bars in federal prisons should be released immediately.

But others that are more abstract will take longer – and require further direction on how to achieve them.

One example from Monday was the order that all agencies should “address the cost-of-living crisis”.

Those that take longer than the four-year presidential term are often overridden if a new president is elected. Many of Mr Trump’s executive orders from his first presidency were focused on undoing the work of President Barack Obama, Mr Biden’s overturned many of Mr Trump’s – and so on.

Can they be overturned?

Congress and the courts have the power to block executive orders – but this is not absolute.

For example, Congress can pass laws to override them but these can still be vetoed by the president.

Congress can also deny the required funding from being allocated.

However, Congressional opposition is less likely this time around, as the Republican Party has control of the House of Representatives, the Senate – and the White House.

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Executive orders are supposed to work within the confines of the law, which means they can also be subject to legal review.

State government officials, campaign groups, and other entities can challenge an executive order if they can prove the president is going beyond his legal powers – or the constitution.

For example, President Harry Truman was stopped from trying to seize steel mills by the Supreme Court during the Korean War after it was argued he lacked the authority to take private property without Congress’s permission.

Will Trump’s latest orders face opposition?

Many of Mr Trump’s latest executive orders are highly controversial.

Although he is less likely to face political opposition due to Republican majorities in Congress, civil rights groups and Democratic attorney generals have already signalled they will launch legal proceedings.

For example, legal action was lodged within minutes of Mr Trump officially ordering the creation of his new Department of Government Efficiency (DOGE) led by Elon Musk on Monday.

Legal action is less likely to be successful when challenging the revocation of Joe Biden’s policies – as these were lawfully approved during his administration.

Opposition groups are more likely to win against the Trump administration’s use of new, untested legal arguments, according to Sky’s US partner network NBC News.

One example is the order rescinding birthrights for children whose parents are not permanent residents or US citizens.

Birthrights – the right of citizenship to anyone born on US soil – come from the 14th amendment of the constitution, which states they apply to anyone “subject to the jurisdiction” of the United States.

Mr Trump’s executive order argues this means it does not apply to undocumented migrants – but legal experts have already indicated the language only refers to those exempt from US law – such as foreign diplomats.

Another example is Mr Trump’s proposed use of the Alien Enemies Act, which is part of the Alien and Sedition Acts 1798.

It gives the president powers to detain or deport foreign citizens during times of war – and was used during the Second World War.

However, Mr Trump’s order will likely struggle to hold up in court – as the US is currently not at war.

Rare winter storms have sparked extreme cold weather warnings – some of the first in history – for parts of the US Deep South.

Lake Charles, Louisiana, had a blizzard warning in place for the first time on record on Tuesday, local meteorologists said.

Historic snowfall of between three and six inches (eight and 15cm) was forecast across Houston, New Orleans, Alabama, and Florida, according to the National Weather Service (NWS).

And Texas was bracing itself for never-before-seen snowfall of one inch (2.5cm) per hour on Tuesday into Wednesday, the forecasters said.

Blizzards are set to bring heavy snow, sleet, and freezing rain all the way along the Gulf Coast from Texas to North Carolina – conditions usually only seen further north.

Meanwhile, Arctic air will also mean colder-than-usual winter temperatures to the US’s east coast and upper Midwest.

Residents in the Dakotas and other parts of the Midwest are being warned of the risks of hypothermia and frostbite amid forecast wind chills of between -34C and -46C.

Thousands of flights cancelled

Almost 2,000 flights were cancelled across the country on Tuesday, with around 10,000 other delays.

Both airports in Houston said they had suspended all flights in anticipation of the bad weather.

Before snow started to fall on Monday, the city’s mayor John Whitmire warned people across the state: “Get prepared to be in your house, in your residence, in your warming place for the next 48 hours.

“Don’t let even clear skies on Wednesday and other days fool you. This is a serious arctic blast.”

Meteorologist Daniel Jones said of record snowfall across the Deep South: “The last time we saw snow of this magnitude was way back in 1960.

“By modern standards this is going to be a historic and very memorable storm for this part of the world.”

States of emergency have been declared by the governors of Georgia, Louisiana, Mississippi, and Alabama, where schools and businesses were told to close.

Ten counties in New York have also put in place emergency measures.

Freezing temperatures saw inauguration proceedings in Washington DC moved inside the Capitol’s Rotunda for the start of Donald Trump’s second presidency on Monday.