He also stirred up a political brouhaha when he suggested that Crimea, an area previously part of Ukraine that Moscow annexed in 2014, rightfully is part of Russia. Mr. Musk’s Starlink satellite-based internet service has been used by Ukraine to battle invading Russian troops, at one point making Mr. Musk something of a hero in the beleaguered country. But the Crimea comment drew pushback from Kyiv, including Ukraine’s President

Volodymyr Zelensky.

Perhaps the most dramatic moment, though, came on Monday, when Mr. Musk notified

Twitter Inc.

TWTR -0.43%

that he planned to go forward with the $44 billion takeover of the business almost three months after trying to abandon the transaction. The surprise about-face came days before Mr. Musk was due to be deposed ahead of an Oct. 17 trial in Delaware Chancery Court, where Twitter had sued to force Mr. Musk to see through the transaction that he tried to walk away from in July.

Behind the scenes, the two parties already had been in talks about closing the deal, first agreed to in April, at cheaper terms, but those discussions went nowhere, The Wall Street Journal reported, citing people familiar with the matter.

Mr. Musk, after his U-turn, tweeted Tuesday that buying Twitter would be “an accelerant to creating X, the everything app.”

What followed were more arguments between the parties, which have been at odds for months. Mr. Musk, in Monday’s letter, had said he would move forward with buying Twitter pending receipt of the proceeds of debt financing, and if the court stayed proceedings. Twitter, in a court filing made public Thursday, pushed back.

“Defendants can and should close next week,” Twitter said. “Until they do, this action is not moot and should be brought to trial.” Mr. Musk countered in his own filing that “Twitter will not take yes for an answer.”

The presiding judge, Chancellor Kathaleen McCormick, on Thursday ruled in favor of Mr. Musk. She gave both parties until Oct. 28 to get the deal done, though also said that should a deal not be reached by then, she would quickly schedule the trial for November.

All the while, Tesla’s shares were falling and ended the week down 15.9%—the worst since the week ending March 20, 2020 and the fourth worst week on record for the stock. The selloff was spurred by third-quarter vehicle deliveries that fell short of what analysts surveyed by FactSet had expected. Some analysts also have said that falling wait times for some Tesla models could signal softening demand. Mr. Musk, the Tesla chief executive, has previously said the business is constrained by production, not demand.

Amid the back-and-forth over the Twitter deal, Mr. Musk also took to the social-media platform to announce that Tesla would deliver its first all-electric semitrailer truck to food and beverage maker

PepsiCo Inc.

in December.

Things were similarly hectic at SpaceX, the privately held rocket and satellite company where Mr. Musk also is CEO. On Wednesday, one of SpaceX’s rockets transported two American astronauts, one from Japan, and a Russian cosmonaut to the ISS. The same day another of his rockets blasted 52 satellites into orbit for the company’s Starlink service.

Space Exploration Technologies Corp., as SpaceX is formally known, has become the world’s busiest launch provider and Mr. Musk has said he wants the pace to increase.

The business isn’t without its challenges. Mr. Musk on Oct. 4 said that Starlink “is still far from cash flow positive,” adding that rival communications constellations had gone bankrupt.

With all that going on, Mr. Musk turned to Twitter as the weekend approached, to reflect: “Very intense 7 days indeed.”

Write to Sarah E. Needleman at Sarah.Needleman@wsj.com