Relatively few shares will be on the open market. If these few shares are sought after (bought by Google), the price will go way higher as more shares are bought out by Google. It's possible to mount actions where things are kept "quiet" and "hard to notice" (See Hermes vs LVMH a few years ago in France) - but even then it can fail (it did). Overall no, you can't buy the whole company at anywhere close to the stock market "market cap". It "works" when the acquirer gets control (enough shares to eventually vote out the current board leadership.)

What sometimes does work is to make a formal offer to buy all the shares that are presented, at some price quite a bit higher than the current market price. Sometimes that works. Occasionally that works for very little above the current market price.

Depends on what % of the company is put on the market. Could Google buy every available share if they are willing to spend enough money? Sure. But if there are not enough shares on the market to give them a controlling interest they still can't hostile takeover that way.

If you mean before the IPO, it depends on the stock plan of the company. They may have clauses that prevent trading on secondary markets. I don’t think this is fair to employees personally, but it is the norm for companies to have various abusive forms of control over the options they grant employees.

That won't be all the shares of the company, just a lot of them. And doesn't give you the control like an acquisition would.