Can a class be declared as static?

No a class cannot be defined as static. Only a method,a variable or a block of code can be declared as static.

How is final different from finally and finalize?

final is a modifier which can be applied to a class or a method or a variable. final class can't be inherited, final method can't be overridden and final variable can't be changed.
finally is an exception handling code section which gets executed whether an exception is raised or not by the try block code segment.
finalize() is a method of Object class which will be executed by the JVM just before garbage collecting object to give a final chance for resource releasing activit

Can you give few examples of final classes defined in Java API?

java.lang.String,java.lang.Math are final classes.

What is the impact of declaring a method as final?

A method declared as final can't be overridden. A sub-class can't have the same method signature with a different implementation.

I don't want my class to be inherited by any other class. What should i do?

You should declared your class as final. But you can't define your class as final, if it is an abstract class. A class declared as final can't be extended by any other class.

What is the purpose of declaring a variable as final?

A final variable's value can't be changed. final variables should be initialized before using them.

What is the access scope of a protected method?

A protected method can be accessed by the classes within the same package or by the
subclasses of the class in any package.