Congress returns this week from its August recess and while the House Intelligence Committee has wrapped up its probe, lawmakers still face big questions regarding the Russian-meddling scandal, threats to the U.S. electoral system, the uses and abuses of social media sites and fresh clashes between the White House and the Department of Justice.

With multiple Senate committee probes and the wider investigation by special counsel Robert Mueller still churning, revelations and events in the coming weeks could have an outsized impact on the GOP’s ability to maintain control of Congress in November’s midterm elections, political analysts say.

Investigators continued to interview key figures during summer recess, including senior Justice Department official Bruce Ohr and former British intelligence officer Christopher Steele over their contacts concerning the controversial dossier Mr. Steele compiled about President Trump’s alleged ties to Russia in the summer of 2016.

In addition, House investigators reportedly traveled to London again to seek out new information about the dossier, which was paid for in part by the Democratic Party and which President Trump and some Hill Republicans contend was served as the spark for the entire Russia probe.

Congressional investigators also requested that WikiLeaks founder Julian Assange, who published thousands of sensitive hacked emails stolen from the Democratic National Committee and Hillary Clinton’s 2016 presidential campaign, testify before the Senate Intelligence Committee.

On Wednesday, social media industry leaders will again be on Capitol Hill to discuss what has and hasn’t been done after the 2016 vote, when Facebook, Twitter, Google and other sites were targeted with Kremlin-produced propaganda aimed at sowing discord, dividing the U.S. electorate, and — U.S. intelligence agencies say — helping Donald Trump at the expense of Hillary Clinton.

The Senate intelligence panel is scheduled to grill Facebook COO Sheryl Sandberg and Twitter CEO Jack Dorsey about their firms’ efforts to increase transparency in political ads and their efforts to crack down on fake accounts, foreign interference and intentionally false news stories.

Google could be represented by an empty seat. Larry Page, the CEO of Google’s parent company Alphabet, was invited but has yet to confirm he will attend. Committee Chairman Richard Burr, North Carolina Republican, has insisted that only top officials testify.

Later in the day, Mr. Dorsey will make a solo appearance before the House Energy and Commerce Committee.

Throughout the day, Republicans are expected to hammer on a fresh complaint from Mr. Trump — that social media firms are allegedly censoring conservative content, “shadow banning,” as Mr. Trump put it, through the use of filters and algorithms.

Mr. Mueller’s Russia probe served up more dramatic moments last month, including the conviction of former Trump campaign manager Paul Manafort on tax and bank fraud not related to his work with Mr. Trump.

But of perhaps greater interest to lawmakers is the guilty plea to tax evasion, bank fraud and campaign finance violations by Mr. Trump’s former personal lawyer and “fixer,” Michael Cohen.

In the wake of the Cohen guilty plea, Senate Judiciary Chairman Chuck Grassley’s staff began talks with Cohen’s attorney, Lanny Davis, about Cohen’s claims that Mr. Trump directed him to pay hush money to two women just before the 2016 presidential election.

The Senate Intelligence Committee is also scheduled to release more of its findings in the weeks ahead, including its analysis of the claims in the Steele dossier, and lawmakers from both chambers are also considering no less than eight separate election security proposals.

Just before their recess, House conservatives also filed articles of impeachment in an effort to oust Deputy Attorney General Rod Rosenstein, for his role in the probe. It is not clear how hard they plan to press their case with Congress returning for a brief session before the midterms.

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