This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
There is one context per "web application" per Java Virtual Machine. (A "web application" is a collection of servlets and content installed under a specific subset of the server's URL namespace such as /catalog and possibly installed via a .war file.)
In the case of a web application marked "distributed" in its deployment descriptor, there will be one context instance for each virtual machine. In this situation, the context cannot be used as a location to share global information (because the information won't be truly global). Use an external resource like a database instead.
The ServletContext object is contained within the ServletConfig object, which the Web server provides the servlet when the servlet is initialized.
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As to your question, what you can set per servlet is, I believe, called servlet parameter, not context parameter. So you can have different servlet parameters for the same servlet class in a web app, but there is only a single context (and its parameters are the same for all servlets).