Whoever is buying the company makes an offer, it can get negotiated by the company/board. Once the negotiations are complete, they can put it up to a vote. Don't overthink this too hard, its not as strange a transaction as you may think.

There are some outlier situations where a certain large shareholder may not get to vote if they have a conflict, but not always. Even as the majority holder, well, in many cases, of course being the majority holder means you can make the decisions, even to sell.

That's not the case here, but in cases where it is there are a few different steps that are put in place: the Board of the target company appoints a special committee that is comprised of people who are not affiliated with the majority owner, the special committee hires an investment bank to evaluate what price would be fair to the shareholders and give a "fairness opinion" that the committee can rely on, the special committee (with help from investment bank and lawyers), and then once a transaction is agreed on its approve "majority of the minority" (i.e. by vote of the shareholders other than the majority shareholder/buyer). Then there are inevitably lawsuits claiming that the transaction was unfair.