When someone talks of servlets and java beans, I guess they are talking of plain java beans and not enterprise java beans (EJBs).
A Java Bean is a reusable software component. It can be a class, applet,application etc...
Java beans wrt servlets/jsp is usually any java class that has set/get properties for attributes and processing methods.
Design Patterns are problem/solution combo for frequently recurring problems in software. Patterns are not specific to EJB.
Enterprise Java Beans specification from Sun represents the industry's best practices and patterns have been incorporated into it.
GOF is the abbreviation for Gang of Four representing the four authors of the first book on Design Patterns published in 1995 , "Design Patterns-Elements of
Reusable Object-Oriented Software" by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides (The Gang of Four). This book is highly recommended for software developers (mainly OO based).
A great place to learn more about java beans, ejb etc is Sun's Java website at http://java.sun.com
Frankly, all of these questions could have been answered if you had just made an internet search on all the key words on Google :-) :-)
Hope you are confused no more. Send me an email with any questions you have.
janilsal <at> yahoo.com