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.

How do I use a scriptlet to initialize a newly instantiated bean?

A jsp:useBean action may optionally have a body. If the body is specified, its contents will be automatically invoked when the specified bean is instantiated. Typically, the body will contain scriptlets or jsp:setProperty tags to initialize the newly instantiated bean, although you are not restricted to using those alone.
The following example shows the "today" property of the Foo bean initialized to the current date when it is instantiated. Note that here, we make use of a JSP expression within the jsp:setProperty action.
value=""/ >

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.