When javascript runtime finds setTimeout() method, it sends it to Event table. How does runtime know that setTimeout() is a WEB API? Does it first look for setTimeout() method in the current context and then if not found assumes it as a WEB API?
In terms of identifying which function to run, it doesn't make any difference whether a function is built into the engine, or added at run-time (this fact is really useful, allowing functions to be "polyfilled" if the engine doesn't provide them).
When you write foo(), JS actually looks for a variable with that name (this unification of variables, properties, functions and methods is an unusual feature of JS). It looks for it first in the local scope, then in the parent of that scope, and so on up the "scope chain".
The last place it looks is the "global object", which in a browser is the window object. So if you define window.foo as a function, you can call foo() from anywhere that doesn't have its own function called foo in scope.
Built-in functions work just the same way: when the JS engine starts up, it (conceptually) defines a whole bunch of functions on the window object, with special implementations referring to internal operations in the engine rather than composed of JS code.
So when you call setTimeout, JS walks up the scope chain, and if it doesn't find anything else, will find the setTimeout function registered by the engine, and runs it. The engine then does whatever it wants to do with that - hopefully, something that complies with the behaviours described in the current ECMAScript standard.