1. Will all of Trump’s nominees be confirmed? And if not, who gets rejected?

On the whole, a new president’s Cabinet picks have been overwhelmingly confirmed: in the last four decades, just five Cabinet secretary picks have withdrawn their names after being nominated and only one (John Tower, George H.W. Bush’s pick for defense secretary) has been rejected by the Senate.

But some of Mr. Trump’s selections -- chiefly ExxonMobil CEO Rex Tillerson for secretary of State -- have seen pushback not just from Senate Democrats, but a handful of Senate Republicans as well. Republicans like John McCain, Marco Rubio and Lindsey Graham have expressed concerns about his ties to and business dealings with Russia.

With a 52-48 margin in the Senate, even a few Republican defections could spell trouble for a Cabinet nominee -- and deal a political blow to Mr. Trump during his early days in office. Will Tillerson be confirmed? And will any other Cabinet nominees have trouble?

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2. What does Trump/GOP Congress accomplish immediately?

When a new president takes office, he (or she) usually has a limited amount of time in which to ride new political capital -- that’s why there’s so much emphasis put on a president’s first 100 days.

Both Mr. Trump and congressional Republicans have outlined a series of top priorities beginning next month: in a November video statement, Mr. Trump said his priorities in the first 100 days include formally withdrawing from the Trans-Pacific Partnership trade deal, canceling environmental restrictions, cut business regulations, enact a lobbying ban for his administration, shore up the country’s defenses against cyberattacks and investigate visa programs and abuses.

In Congress, House Speaker Paul Ryan has said that repealing the Affordable Care Act is priority number one.

Which of those things happen first, and which of them ultimately take longer to accomplish?

3. Can the Republican Party hold together? And if not, what’s the first issue to divide Trump and the GOP?

Despite many Republicans’ objections to Mr. Trump, he ultimately gave them their wildest dream on Election Day: not only the White House, but both houses of Congress. In the wake of that victory, many Republicans -- including Ryan -- have buried the hatchet with Mr. Trump in the hopes of working together.

But the fact remains that the Republican Party spent much of 2016 having a battle over its identity and its future -- and that doesn’t just get buried now that Mr. Trump is taking over at the White House and other Republicans want to make nice with him. Mr. Trump has some serious political and policy differences with Republican orthodoxy, from his stance on trade agreements to his views on Russia.

How able is the Republican Party to stay united once they hold the reins to govern? And if we do see a major split between the Trump White House and the GOP-led Congress, what’s the first issue to cause it?

4. Who becomes the de facto leader of the Democratic Party?

With Hillary Clinton’s loss and President Obama’s imminent departure from the White House, the Democrats are a party without a leader. This is true in a broad sense, but is also literally true: the Democratic National Committee is in the midst of a race to elect its next chair, a race that says a lot about where the party is headed.

As Democrats contend with a President Trump early next year, they do so without a unified strategy for combating Mr. Trump -- and without anyone to articulate that strategy.

Who steps up to fill the party’s leadership void?

5. What lessons (if any) does the Democratic Party take away from Hillary Clinton’s loss?

As was just mentioned, Democrats are in the midst of a campaign for their next DNC chair -- a race that is in many ways a proxy war between wings of the Democratic Party who envision very different futures for the party.

There’s one school of thought that says Democrats neglected the white working-class voters by focusing too much on identity politics in an attempt to recreate the Obama coalition. Others say the 2016 loss was more the result of Clinton’s inability to energize and mobilize that Obama coalition. Democrats on the more establishment side hint that the party may need to moderate some of its views; progressives argue that the party must move left, particularly on economic issues, in order to reach more lower-income voters.

Who helms the DNC says a lot about what the Democratic Party message will be going forward and whether the party learns the right kinds of lessons from 2016.

6. If Republicans repeal the Affordable Care Act, what will they replace it with?

Republicans will control the White House and both houses of Congress for the first time since 2006 -- and congressional GOPers have made it clear that repealing the Affordable Care Act is among their very highest priorities.

But it’s still unclear exactly what Republicans would do as an alternative. Some members -- including Mr. Trump’s pick for the Department of Health and Human Services, Rep. Tom Price (R-Georgia) -- have put forth proposals, but there’s been no real indication of a party-wide consensus around any particular solution. On the campaign trail, Mr. Trump said the replacement would be “fantastic” but had few -- if any -- details of what the replacement might entail. “We’ll have private health care, but I will not allow people to die on the sidewalks and the streets of our country if I’m president,” is how he put it at one Republican primary debate last February.

As discussions about repealing the ACA get real under a new Congress, what kind of health care plan do Republicans propose? And can Mr. Trump and the GOP Congress agree on one?

7. What is Trump’s first big unexpected test?

Every president deals with unexpected crises -- the kinds of things that former Defense Secretary Donald Rumsfeld referred to as “unknown unknowns.”

For President Obama, some of those crises have included natural disasters (Hurricane Sandy and Hurricane Matthew, for example), major pandemics (Ebola, Zika) and terror attacks (the Orlando shooting, the San Bernardino shooting, and more).

How a president reacts to situations outside his or her control says a lot about the kind of person and the kind of leader they are. What will Mr. Trump’s first big test be, and how does he handle it?

8. Does Russia become a U.S. ally?

It’s no secret that Mr. Obama and Mr. Trump hold drastically different views on a whole host of political and policy questions -- but perhaps nowhere is that difference more pronounced than when it comes to the U.S. relationship with Russia.

With U.S. intelligence agencies alleging that Russia deliberately worked to influence the U.S. election in Mr. Trump’s favor, that divide has become even clearer. The Obama White House is currently readying a response to Russia over the hacking allegations, and Mr. Obama has spoken harshly about Russian President Vladimir Putin’s attempts to meddle on this side of the Atlantic.

On the other hand, Mr. Trump has dismissed the CIA and FBI’s assertions and said Democrats who accuse Russia are politically motivated. Trump also repeatedly spoke of his desire for the U.S. to have a better relationship with Putin on the campaign trail, and has been largely unwilling to criticize the Russian leader.

What does the U.S.-Russia relationship look like under Mr. Trump? Does he get as close with Putin as his words and actions have suggested he will?

9. Which campaign trail promises does Trump break once he’s in office? And do his supporters care?

Mr. Trump began backtracking on his campaign promises just days after being elected: he suggested there might be parts of the Affordable Care Act he’d be interested in keeping, said he doesn’t actually plan to appoint a special prosecutor to investigate Clinton, and has said the U.S.-Mexico border wall that was a centerpiece of his campaign could include some fencing.

New presidents frequently change their tune a bit after getting elected. But some of those shifts have already begun to rankle his supporters, many of whom took him at his word when he said he planned to “Lock her up” (regarding Clinton) or build that wall. And as Mr. Trump adjusts to the reality of governing, there will surely be other campaign promises that don’t ultimately happen.

The question is just how many of those broken campaign promises there are -- and whether his supporters understand and stick by him.

10. Does the “Trump phenomenon” continue worldwide?

Mr. Trump himself has referred to his victory as “Brexit plus-plus-plus” -- a nod to the United Kingdom’s vote last June to leave the European Union. Both the Brexit vote in June and Mr. Trump’s victory in November have been seen as the potential start to a rise of right-wing populist movements across the Western world.

It’s unclear whether other populist movements will triumph or collapse, however. Earlier this month, Austrian voters rejected the Freedom Party’s Norbert Hofer, who would have been the first far-right head of state in Europe since World War II; the same day, Italians voted against a set of proposed constitutional reforms that resulted in the resignation of prime minister Matteo Renzi, which was seen as victory for populists.

Next year, far-right populism will get tested at the ballot box in a handful of important European countries. On March 15, the Netherlands votes in its general election, with the Freedom Party’s Geert Wilders, a populist running on an anti-immigration platform, potentially poised to become prime minister. In April and May, far-right French National Front leader Marine Le Pen is likely to advance to the final round of France’s presidential election. And in the fall, German Chancellor Angela Merkel and her Christian Democrats will face the growing momentum of the far-right, anti-immigrant Alternative fur Deutschland (AfD).

Which places see big victories for far-right groups -- and how does that shape the group of world leaders that used to include people like Mr. Obama, Renzi and the UK’s David Cameron?

CBS News’ Steve Chaggaris contributed to this story.