The question does not specify a jurisdiction and I am answering primarily based upon U.S. law. But, I have no good reason to believe that the law in most other countries that have publicly traded corporations would be different.
if a major shareholder of a large corporation (say 15%) meets with a
CEO candidate without the board's knowledge or discretion and offers
that candidate options to entice them to join the company, this would
be considered unethical or even illegal. Is that correct?
This would not necessarily be either unethical or illegal. The shareholder couldn't obligate the corporation to provide those options, but the shareholder could buy those options personally and the give them to the CEO candidate if the CEO candidate accepted the job.
In general, a shareholder owes almost no duties to anyone (except not to oppress minority shareholders), and since this doesn't appear to be oppression of minority shareholders, the shareholder hasn't breached any duty.
The CEO would probably have an obligation under the applicable securities laws to disclose the existence of the options the CEO received if the CEO candidate got the jobs and the options, in a publicly held corporation. But, generally speaking, owning stock options in a a company in which you are a CEO is not a violation of any duty of loyalty owed by the CEO or CEO candidate to the Corporation (to whom CEOs owe almost all of their duties).
As long as the CEO candidate doesn't promise the shareholder donor that the CEO will do something illegal, or something contrary to the best interests of the company as the CEO sincerely believes them to be, this wouldn't obviously be either a crime or a civil wrong.
Of course, if there was a promise to do something illegal it would constitute a conspiracy or solicitation of a crime or tort, giving rise to criminal or civil liability as the case might be to both parties.
Likewise, if there was a promise to do something the CEO believed was clearly contrary to the best interests of the corporation, this would probably be the crime of commercial bribery, or the tort of interference with contract by the shareholder and a breach of a fiduciary duty of loyalty by the CEO, and might also constitute securities fraud via market manipulation in some circumstances.
In real life, there might also be situations where the CEO either promises to do something, or is motivated to do something, that isn't clearly contrary to the best interests of the corporation in the CEO's opinion, but also wasn't precisely what the CEO sincerely believed was in the best interests of the corporation (e.g. hiring the donor shareholder's nephew to be a junior executive of the corporation, when the nephew wasn't incompetent but also wasn't the most qualified candidate for the job). This kind of gray area would typically not give rise to criminal or civil liability in a publicly held, for profit, corporation, which is very hard to establish in court even in clear cases, even though this kind of conduct that is a gray area in a for profit corporation might be clearly illegal if it took place in a governmental agency (see the endnote below).
Without these improper promises, however, few people would consider it unethical either. Indeed, arguably, the shareholder is going "above and beyond" ethically by using the shareholder's personal resources to help a business the shareholder has invested in without getting anything directly in return for this contribution from the corporation, the other shareholders or the CEO (all of whom benefit from the gift of the options). It isn't really different in principle from holding a welcoming banquet to a new CEO without charging the corporation for the event. Whether that was a gift or compensation for tax purposes would be a hard question that I won't even attempt to answer.
In closely held companies, transactions like this wouldn't be terribly uncommon.
if the major stockholders choose to not sit on the board for some
reason (even someone who owned 51% of all stock), would this mean they
cannot make major decisions for the company even though they own the
majority of the shares?
Shareholders get to vote in elections for the board of directors, and to vote on resolutions presented to the shareholders such as amendments to the articles of incorporation and board policy issues presented to shareholders by either the board of directors or blocks of shareholders who present the issue to the shareholder.
Typically, a shareholder with a large percentage of stock (a 10% threshold would be pretty common but each company's bylaws would determine the exact amount), can also convene a special meeting of the shareholders to conduct any business that the shareholders have the authority to conduct, including, in most cases, a vote on removing members of the board of directors without cause and replacing them with new directors.
These are pretty major decisions.
Also, since every member of the board will typically owe their appointment in part to the support of the large shareholders in the company (in practice, of course, directors are almost always elected unanimously on a Soviet ballot with only one candidate for each position), every director will normally be very solicitous of a large shareholder's opinions on corporate decision making even though they are legally bound to follow any particular large shareholder's directions, even if the shareholder owns a majority or supermajority of the outstanding shares.
In particular, there are two parts of the United States Constitution that address situations like these for certain federal employees: "the Foreign Emolument Clause and the Presidential Emolument Clause. The first of these provisions prohibits any "person holding any office of profit or trust under [the United States]" from "accept[ing]… any present, emolument, office, or title, of any kind whatever, from any king, prince, or foreign state" without Congressional consent. And the second prohibits the President from receiving "any…emolument" from the United States or any of the states, other than his official compensation."