Can we use the constructor, instead of init(), to initialize servlet?

Yes , of course you can use the constructor instead of init(). There’s nothing to stop you. But you shouldn’t. The original reason for init() was that ancient versions of Java couldn’t dynamically invoke constructors with arguments, so there was no way to give the constructur a ServletConfig. That no longer applies, but servlet containers still will only call your no-arg constructor. So you won’t have access to a ServletConfig or ServletContext.

Can a JSP page instantiate a serialized bean?

No problem! The use Bean action specifies the beanName attribute, which can be used for indicating a serialized bean.
For example:
A couple of important points to note. Although you would have to name your serialized file "filename.ser", you only indicate "filename" as the value for the beanName attribute. Also, you will have to place your serialized file within the WEB-INFjspbeans directory for it to be located by the JSP engine.

Why is _jspService() method starting with an '_' while other life cycle methods do not?

_jspService() method will be written by the container hence any methods which are not to be overridden by the end user are typically written starting with an '_'. This is the reason why we don't override _jspService() method in any JSP page.