Err, you might want to at least watch Succession if you can't keep up with the IRL drama.
In September 2023, News Corp reported that Rupert Murdoch would retire from the board of News Corporation. He would also retire from the board of Fox Corporation and his son Lachlan Murdoch would replace him on both boards. The retirement would take effect in November 2023.
You're probably right. I trusted Google's summary: "Rupert Murdoch's News Corp owns the British newspaper The Times and its sister paper, The Sunday Times. Both are published by Times Newspapers Ltd, a subsidiary of News UK." which might be incorrect.
That's all correct. The only slightly questionable bit might be control of News Corp, but, realistically, it's not unreasonable to consider it to still be Rupert Murdoch's.
The siblings voting rights in NewsCorp are inactive / on hold or somesuch and Lachlan has his block and his dad's, and there's a slew of detail.