I don't see how they have a monopoly on the search engine market. It is definitely the most popular and probably the best search engine, but there is definitely no limit on other adequate alternatives. A monopoly occurs when a company controls a product or service significantly enough to significantly control the terms people must follow access it. Google hardly does this. Most people might choose them, but they don't need to in order to access a search engine. For example, if tomorrow Google decided to start charging a buck a search, 99.9% of their users would instantly switch search engines with very little ill effects.
Heh, try this for size: "I don't see how they have a monopoly on the operating system market. It is definitely the most popular and probably the best operating system, but there is definitely no limit on other adequate alternatives"
Microsoft got into trouble because they leveraged the popularity of one product (Windows) to push another (IE). Google will be fine provided they never release a feature on their website that requires Chrome. At that point, what's sauce for the goose is sauce for the gander.
But IIRC, windows/IE was different: how easy was it for the typical person to run a computer without windows as their operating system? Not very, unless they bought one brand of product (Apple). However, for every service google offers, there are multiple and easily accessible alternatives. With most ISPs, Google isn't even the default search engine out of the box.
Google wouldn't make a Chrome-only feature, simply because then it wouldn't be available to the massive user base which doesn't use Chrome. Which is most people right now, and will probably continue to be most people.
I think that depends. If Chrome actually enabled features otherwise impossible, they might. At least they'd have a rational reason too (as would all developers). Maybe Gears is more of a candidate for this.