Handling multiple requests(different or of the same type) in the same Java Servlet, how to?

Question

so what i am trying to do is , i have 2 html pages - 1 allows to search users in DB by email and 1 by ID. So i have 2 forms on each to let user insert a number and a String.Now i want the request made on each of this 2 pages to go to the same servlet for different processing , is that possible?

This is the servlet that redirects to 1 of the 2 html pages with the search forms, namely searchbyid.html and searchbyemail.html.

public class SearchServlet extends HttpServlet {
    public void doPost(HttpServletRequest request, HttpServletResponse response) throws IOException, ServletException {
        String value = request.getParameter("searchType");
        RequestDispatcher view;
        if(value.equals("ById")){
            view = request.getRequestDispatcher("searchbyid.html");
            view.forward(request, response);
        }else{
            view = request.getRequestDispatcher("searchbyemail.html");
            view.forward(request, response);
        }

        Utils.searchBy(request, response);
    }

Here are my 2 forms: The search by id form is on "searchbyid.html".

<div id="container">
    <form method="POST" action="ResultServlet">
        <p>
            <label for="searchId">Please enter user id</label>
            <input id="searchId" name="searchId" type="text">
        </p>
        <p>
            <input id="submitButton" type="SUBMIT">
        </p>
    </form>
</div>

Now the second form, searching by email is on searchbyemail.html.

<div id="container">
    <form method="POST" action="ResultServlet">
        <p>
            <label for="searchEmail">Please enter user E-mail:</label>
            <input id="searchEmail" name="searchEmail" type="text">
        </p>
        <p>
            <input id="submitButton" type="SUBMIT">
        </p>
    </form>
</div>

The fix for my problem would be to create 2 servlets for each form, but i do not want to do that.I want to create a single servlet wich will handle both forms even if they come from 2 different html pages. Now my questions are:

1.Can a servlet only have 1 doGet and 1 doPost?is overloading possible?

2.Should i use GET or POST for the forms and why?

3.Should i use GET method for one of the forms and POST for the other one in the same servlet?

4.Is there a way to make a doXXX method accept different requests?

5.What would be the most elegant solution to make 1 single servlet manage both forms without using any framework - just servlets and html/jsp?