(CNN) Donald Trump's young presidency has been marked by palace intrigue, a wave of public squabbles with government agencies, rogue social media accounts and critical news reports press secretary Sean Spicer called "demoralizing" to the White House.

Less than a week after he was sworn in, Trump has been at the center of an assortment of behind-the-scenes dramas -- and a few curious comedies. Meanwhile, his family and their smartphones have assumed the work of crafting a softer image for the pugnacious president.

As this whirlwind first week comes to a close, here are seven story lines to watch -- and remember.

Home alone -- and ready to entertain

With first lady Melania Trump and son Barron back in New York City, the White House's newest full-time resident is rolling out the welcome mat for Washington's elected elite, CNN's Jeff Zeleny reports. He entertained congressional leaders on Monday during an off-hours meet and greet and is expected to dole out more invitations in the coming weeks.

"It's very good -- a beautiful relationship," he said as visitors passed through during that first get-together. Nearby, a piano player dialed up Billy Joel's "New York State of Mind."

The legend of Bernhard Langer

But a digression from the light banter with his new friends from Capitol Hill set off an odd debate surrounding Trump's insistence -- absent any evidence -- that his loss in the popular vote was the result of more than 3 million "illegals" casting ballots for Hillary Clinton.

When top Democrats in the room pushed back, Trump sought to backstop his story with the tale from Bernhard Langer, the German golfer, The New York Times' Glenn Thrush reports.

German golfer Bernhard Langer disputed Trump's account.

Langer, the story went, had told Trump that he was prevented from voting on Election Day while others in line at his polling place -- including many of Latin American provenance -- were permitted to cast suspect ballots.

The yarn did not play well in the room and by early Thursday, Langer himself had issued a statement attempting to correct the record.

"The voting situation reported was not conveyed from me to President Trump," he said, "but rather it was told to me by a friend. I then relayed the story in conversation with another friend, who shared it with a person with ties to the White House. From there, this was misconstrued."

It's worth noting -- as Langer did in the next sentence -- that he is not a US citizen and cannot legally vote.

Hanging Andrew Jackson

First he swapped his predecessor's red curtains for Trumpian gold and restored a much worried over bust of Winston Churchill to the Oval Office. But the 45th president's most eye-catching addition is a portrait of the seventh, Andrew Jackson.

"A lot of people, they compare the campaign of Trump with the campaign of (Jackson)," Trump told ABC during an interview Wednesday night. "You have to go back to 1828, but that seems to be a comparison for certain obvious reasons."

Jackson was elected in 1828 after a narrow defeat four years earlier, and is widely regarded as the first political populist to ascend to the presidency. But his best known campaigns were waged on the ground -- first as a general during the War of 1812, then against the Native American population, which he ruthlessly sought to purge from its ancestral homes east of the Mississippi River during his time in the White House.

A stairway divides them?

Access to the President is the most valuable commodity in any White House and, for all its quirks, Trump's is no different. The conventional wisdom is that son-in-law Jared Kushner is the one who gets the final word, with chief of staff Reince Priebus and chief strategist Steve Bannon close behind.

JUST WATCHED Who's near Trump in the new White House? Replay More Videos ... MUST WATCH Who's near Trump in the new White House? 00:48

But what of Kellyanne Conway, campaign manager turned counselor to the president, and the person most willing to publicly argue the administration's case?

It's hard to ignore the suggestion that her new office -- on the second floor of the West Wing -- might be a sign of diminishing influence. The Washington Post, in a wild account of the administration's first week , cited a presidential "confidant" who "dismissively predicted that Trump would rarely climb a flight of stairs."

The longest photo shoot

If the past seven days have been any indication, the style of the Trump White House will be shaped -- and shared -- by his children and grandchildren.

First daughter Ivanka moved with husband Jared to Washington ahead of the inauguration and her Instagram snaps have already begun to present an idealized picture of her father's administration.

Heading to the parade! 🇺🇸 #inauguration A photo posted by Ivanka Trump (@ivankatrump) on Jan 20, 2017 at 12:31pm PST

And she's not alone. Daughter-in-law Lara Trump, married to Eric Trump, also keeps a busy social media schedule.

When aunts and uncles attack! 😜 A photo posted by Lara Trump (@laraleatrump) on Jan 23, 2017 at 5:35am PST

Their quest to create a modern day Camelot should at least keep the local gossip columns and celebrity magazines stocked with high quality, filtered reproductions of the Trump clan's comings and goings.

The President and the press secretary

The state of play with press secretary Sean Spicer is less peachy. A longtime Washington media professional, Spicer's credibility has taken more shots in the past week than it did during years in the partisan trenches.

In a blazing Saturday debut, he stated the Friday crowds has been "the largest audience to ever witness an inauguration — period — both in person and around the globe," then promptly left the briefing room without taking questions.

JUST WATCHED Spicer: Inauguration had largest audience ever Replay More Videos ... MUST WATCH Spicer: Inauguration had largest audience ever 01:13

Conway on NBC's "Meet the Press" the next day said Spicer had simply presented "alternative facts" -- sparking equal or great incredulity -- in support of Trump's enduring belief that his inaugural crowd was bigger than it actually was.

But at least he earned the boss's roaring approval, right?

Not quite.

One White House source told Axios , a new Washington news outlet, that Trump was unimpressed -- with Spicer's suit styles. Another account, in the New York Times, cited multiple sources who said said the press secretary had, in Trump's opinion, gone "too far."

About those press relations...

Spicer has done his best to play nice, or at least adhere to the norms of the job, in the aftermath of his Saturday blitz. But other senior members of the new White House seem less inclined to the Trump-media "co-parenting" agreement being pushed by Conway during an inteview with Fox News' Sean Hannity.

"This White House and the media are going to share joint custody of this nation for eight years, and we ought to be able to figure out how to co-parent," Conway said.

In a rare interview, Bannon, the former Breitbert executive and alt-right champion, told The New York Times that "the media should be embarrassed and humiliated and keep its mouth shut and just listen for a while."

"The media here is the opposition party," he continued, expressing a mix of distress and anger that news outlets had not separated out the unbelievers and "fired or terminated anyone associated with following our campaign."

He then claimed, without naming names, that the press had been cheerleaders for Clinton, and "that's why you (the media) have no power."

The comments, published Thursday, were made Wednesday -- a little more than 100 hours into the Trump presidency.