The former White House aide said the Kremlin had been "mucking around" in elections for decades.
The pair joked about the perfect-looking pie the press secretary baked.
The NFL free agent has been named GQ's Citizen of the Year.
Demonstrators were reportedly pepper sprayed and kettled.
Edith Macias was charged with the misdemeanor of petty theft following the incident.
The president maintained Moore had denied the allegations.
Trump's son-in-law reportedly asked a friend about the reach of the investigation.
The president also said he would be a “much nicer” leader than Truman, who did not pardon any birds.
The president said people were taking advantage of the system.
The SNL skit suggested everything from nuclear war to pets as reasons to miss the ex-president.
The first family is not expected to be at the White House over the holidays.
His comments appeared to be a nod to the deployment of three Navy aircraft carrier groups to the Korean Peninsula last month.
The president was the winner of the 2016 accolade but seems unlikely to make it two in a row.
President Trump has made his feelings towards the mainstream media clear.
The president suggested the athletes should have been left in China after the parent of one player downplayed his role in the matter.
The former strategist said the grassroots movement scares people.
More than 1,900 homicides have been registered in Guerrero state this year.
Moore has been accused of sexual misconduct by five women, one of whom claimed she met Moore when she was just 14 years old. Moore has denied the allegations.
“What does Ali Velshi’s background have to do with dating children,” MSNBC host Stephanie Ruhle asked attorney Trenton Garmon.
Sixty percent of American voters feel the investigation is being conducted fairly, a poll shows.