How many JavaScript programs are executed for a single web-page in the browser?

Dmitry Soshnikov has answered your question. Every <script> element is executed as a Program, as defined by the ECMAScript specification. There is one global object that each Program within a single page uses. And that's really it.

Function hoisting — the process that evaluates function statements before the rest of the function — is part of the ECMAScript standard IIRC (I can't find a reference right now, but I recall seeing discussions of EMCAScript that mention it). The evaluation of script tags is part of the HTML standard. It does not specify that they are "separate programs" in so many words, but it does say that the script elements are evaluated in the order they appear in the document. That is why functions in later script tags aren't hoisted: The script hasn't been evaluated yet. That also explains why one script stopping doesn't cut off subsequent scripts: When the current script stops evaluating, the next one starts.

They are separate programs, but they modify a shared global object.