The relevant law is Section 2 of the Sherman Antitrust Act of 1890. The elements for contravening it are:
- the possession of monopoly power in the relevant market; and
- the willful acquisition or maintenance of that power as distinguished from growth or development as a consequence of a superior product, business acumen, or historic accident.
Google is not an illegal monopoly primarily because its present market position is the result of "a superior product, business acumen, or historic accident."
Whether it is a practical monopoly depends on how you define the market. I'll start by stating that there is no "search engine market" because the users of search engines do not pay for that service. The market that Google is part of is the advertising market.
So, having decided that, how does one define the market? If you define it as the market for advertising on search engines then Google has significant market power. However, if you define it as all advertising - search-engine, website adds, Facebook/Twitter etc. feed advertising, print media, television, cinema, radio etc. then, while still a large player, Google is well short of a monopolist.
As to your particular questions:
Is there a fixed threshold of market share above which you are considered a monopoly (for example, 80%?)
No. "Monopolize" is not defined in the act but the courts have held that a business is a monopoly when it can exercise monopoly power, primarily, that it can charge monopolistic prices because consumers lack alternative substitute goods or services. As such, there is no fixed percentage.
How is a market delimited?
Defining the boundaries of "the market" is a major part of these types of court cases. Modern decisions tend to be sophisticated and are based on answering the question: "If a consumer cannot buy this good or service, what alternative goods and services could they buy to achieve the same objective?"
For example, sea freight, road freight and air freight might be a single market or they might be three (or more) different markets depending on what is being transported. For example, sea freight is not a substitute for air freight for highly perishable goods (like radioactive isotopes or fresh fish) and air freight is not a substitute for sea freight for very heavy items (like motor vehicles) but they might be substitute for other things (like smart phones).
Can Google elude accusations of being a monopolistic search engine by simply expanding its operations to other fields (automobile, consumer electronics) and define itself as more generic company?
No. Monopolies are defined market-by-market, not by how many markets a business operates in.
Can a company be legally deemed a monopoly but still not subject to any punishment because it is not using the power derived from this monopoly to influence market fairness?
Yes. That is the second element required before the operations become illegal; a monopolist must have either acquired their monopoly power willfully or, once acquired, use it in an illegal way.
A "benign" monopoly does not fall foul of anti-trust law but it can still be broken up by legislative action.