New York – Americans may still be divided on Donald Trump, their new president, but the rest of the world has seemingly made up its mind. A Pew Research Center survey across 37 countries found that respondents broadly view him as "arrogant, intolerant and even dangerous".

The Republican's plans - which include walling off Mexico, scrapping the Paris climate change deal and imposing a 'Muslim Ban' on travellers from six predominantly Muslim countries - left only 22 percent of Pew's respondents with confidence that Trump would "do the right thing" on the world stage. His predecessor, Barack Obama, a Democrat, scored a median of 64 percent in his final years.

Not surprising, then, that Trump's second foreign trip will be eyed closely. He is set to speak in Warsaw, Poland, about Washington's security policy along Russia's western flank this week and then will convene with leaders of the world's top G20 economies in Hamburg, Germany on Friday and Saturday.

There, he will rub shoulders with political heavyweights, from the host, German Chancellor Angela Merkel, to Chinese President Xi Jinping and hold a much-anticipated maiden face-off with Russian President Vladimir Putin.

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The agenda is packed with hot-button issues, from immigration to trade protectionism, the environment, North Korean nuclear arms, and Syria's civil war. Therein lies a problem, Matt Goodman, a former White House adviser, told Al Jazeera.

"There's always a possibility for breakthroughs, but I'd say the greater likelihood is of some sort of dust-up, most likely over trade or climate change," said Goodman, who helped Obama prepare for summits during his presidency.

Tens of thousands of protesters are expected to rally in a city that is a hotbed of anti-capitalist feeling, including hundreds of people dressed as zombies. Here, Al Jazeera highlights the key issues for the coming days.

1. EUROPEAN DEFENCE

Six weeks ago, Trump scolded NATO leaders in Brussels for failing to spend enough on defence during a speech in which he pulled back from explicitly endorsing NATO's Article 5, the collective defence provision of the treaty that is the bedrock of the Western security framework.

Since then, NATO Secretary-General Jens Stoltenberg has sought to answer Trump's grievance by outlining a 4.3 percent "significant increase" in defence spending among allies of the 29-nation bloc this year.

Trump will meet leaders from central Europe, Baltic States and the Balkans in Warsaw on June 6 and deliver a speech which, according to National Security Adviser HR McMaster, will "lay out a vision, not only for America's future relationship with Europe, but the future of our transatlantic alliance".

Jeff Rathke, a former US State Department official, told Al Jazeera it is still not clear what Trump will say.

"The question is: can Trump take yes for an answer? Will he welcome the spending increases or will he double down and call for more?" Rathke said, adding that European leaders will be "biting their nails" in anticipation of an explicit recommitment to Article 5.

The location is key. Despite doubts elsewhere, the US remains relatively popular in Eastern Europe, where Russia's annexation of Crimea in 2014 and muscle-flexing is viewed warily. Poland already meets its NATO spending goals, hosts some 1,000 US troops and is eager to buy liquefied natural gas from US firms to counterbalance Russian gas supplies in the region.

2. TRADE AND CLIMATE CHANGE

At the G20 summit on June 7-8, Trump will encounter leaders of long-standing US allies who question his stewardship of the world economy, including French President Emmanuel Macron, with whom the US leader had a strangely competitive public handshake in May.

Trump's "low popularity among Europeans makes it difficult for some democratically elected leaders there to risk aligning with the US", said Rathke. This goes for Merkel, who must be "defender" of the global bodies that Trump bashes to boost her re-election chances this year.

The German has blasted Trump's team for its "winners and losers" approach to diplomacy. She has put climate change high on the G20 agenda, and derided Trump's withdrawal from the landmark Paris climate agreement in June.

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"We'll be watching to see whether a G19 of other leaders gets behind a statement that further isolates the US position," Sarah Ladislaw, an expert at the Center for Strategic and International Studies, a Washington-based think-tank, told Al Jazeera.

Trump's trade protectionism is another issue. Following a national security review, he is expected to demand action by G20 leaders to reduce excess capacity and other distortions in the global steel market, and is mulling a 20 percent tariff on imports of the alloy to the US.

"That's going to hit not just China, which may have been the original impetus for the review, but also many allies who supply most of our steel, such as Canada, Germany, Japan, Korea, and others around that table," Goodman told Al Jazeera.

3. NORTH KOREA

Trump seemingly struck up a 'bromance' with his Chinese counterpart, Xi, during a two-day summit at the billionaire's Florida residence, Mar-a-Lago, in April. Trump made grand gestures for warm ties and later called Xi a "good man".

He brushed aside earlier criticism of Beijing as a "currency manipulator", angling for Chinese pressure to halt North Korea's race towards developing nuclear warheads and the missiles that can reach the US mainland.

That relationship has since soured, with Trump regarding Xi as dragging his feet on Pyongyang and the US selling weapons to Taiwan.

The two men will meet at the G20 in the wake of Tuesday's test by Pyongyang of a newly developed intercontinental ballistic missile that analysts say may be capable of striking Alaska - raising the stakes once again.

4. US-RUSSIA TIES

It could be the most eagerly-anticipated political showdown of 2017.

The first face-to-face meeting between Trump and Putin on the sidelines of the G20 comes against a backdrop of competing US-Russia interests in Syria's civil war and allegations of Russian meddling in last year's US election.

Trump is under domestic pressure to take a tough line with Putin. US legislators are pushing new sanctions against Moscow; while Trump's campaign team is being probed for colluding with Kremlin-backed hackers who allegedly tipped the vote in their favour.

Reporters will not likely learn much about a meeting that takes place behind closed doors, but will doubtless dissect any outward signs of chumminess or frostiness between the two alpha-males that the cameras capture.

"From the outside, it's a crazy spectacle," Nicolai Petro, a University of Rhode Island scholar, who is currently based in Ukraine, told Al Jazeera.

"The world is hoping that whatever cleansing needs to happen in America happens fast so that the United States can get back to having businesslike relations with Russia, China and other countries."

5. GLOBAL LEADERSHIP

Underpinning all of this is a broader question over whether the US, under Trump, is abrogating its role as guarantor of global security and economic cooperation that it has built since the end of the second world war.

As Trump criticises US allies as freeloaders and tears up trade deals, such as the Trans-Pacific Partnership, analysts assess whether he marks an end to the post-war order, or just a temporary glitch until somebody else runs the West Wing.

Meanwhile, Xi has vaunted China as a leader on climate change and open markets. Merkel has been praised for welcoming refugees to Germany, though Berlin carries neither the military nor economic weight to supplant the US.

According to analysts, we will have a stronger idea of this trajectory after Trump speaks in Poland. As it stands, the "administration hasn't articulated a positive vision of its foreign policy or the concrete achievements it seeks", said Rathke.

According to Petro, seven decades of US hegemony will not evaporate any time soon.

"Some European leaders seem to have given up on Trump, but there's really no alternative to US leadership," Petro said.

"Global institutions are structured in such a way that Europe has seldom acted decisively or independently. That is why Trump is being dragged, kicking and screaming, back to a position of leadership."

Follow James Reinl on Twitter: @jamesreinl