you can write as like for regular class.

No..not at all,,,,servlet is a class which is dynamically 
loaded...dynamically loaded class never requires 
constructors.

constructor required, but it should be public no-argument
constructor. even though if you are not write that
constructor   java compiler will create that construtctor by
default. for that your servlet class should be public other
wise you will get RuntimeWxception saying RequestedResource
is not available  like that.

yes offcourse you can write a constructor for a servlet
after all it is a java class. you can simply provide but if
u do not provide then it is by default include the no
argument constructor that is used by the Init() method in
the servlet life cycle.

yes, we can write constructor on our own but it should be 
no argument public constructor only, cause container will 
create the object so it needs no argument constructor.

yes., when ever the servlet is executed .,it requires 
configuration.,the configuration should be done in init() 
method only.,