How to update a selectonemenu depending on other one selected value?

Question 1

value="municipio" in <p:selectOneMenu id="Municipio" value="municipio"> means that the value in that dropdown will never change as you've effectively hardcoded the value on that field to always be municipio (and even that will fail conversion). The value attribute should be bound to a backing bean variable as in
```
  <p:selectOneMenu id="Municipio" value="#{beanInscripcion.municipio}" >  
    <f:selectItems value="#{beanInscripcion.municipios}"  
                   var="mun" itemLabel="#{mun.nombre_municipio}" itemValue="#{mun.nombre_municipio}" />  
</p:selectOneMenu>
```
and in your backing bean, have
```
   Municipio municipio;
  //getter and setter
```
Remove the parameter event from <p:ajax update="Municipio" listener="#{beanInscripcion.buscarMunicipios(event)}" />. It should be
```
<p:ajax update="Municipio"  listener="#{beanInscripcion.buscarMunicipios}" />
```
Remove valueChangeListener="#{beanInscripcion.buscarMunicipios(event)}". It's unnecessary because you already have a <p:ajax/> event defined
You will eventually run into problems submitting that form because you haven't created a JSF Converter for that Municipio custom type. It's mandatory if you're using anything other than String types in your select components. See a short intro to converters/converting here

Question 2

I am using Primefaces and this is pretty simple. I have 2 seleceOneMenus, one for subjects (the parent one) and another one for Topics (the child one.).

<h:selectOneMenu id="subject" value="#{QuestionsMB.selectedSubjectId}" var="selectedSubject">  
                <f:selectItem itemLabel="Select Subject" noSelectionOption="true" />
                <f:selectItems value="#{SubjectsMB.subjectsList}" var="selectedSubject" itemValue="#{selectedSubject.id}" itemLabel="#{selectedSubject.subjectName}" />
                <p:ajax update="topic" />
            </h:selectOneMenu>


            <h:selectOneMenu id="topic" value="#{QuestionsMB.selectedTopicId}" var="selectedTopic">  
                <f:selectItem itemLabel="Select Topic" noSelectionOption="true" />
                <f:selectItems value="#{TopicsMB.getTopicsListBySubjectId(QuestionsMB.selectedSubjectId)}" var="selectedTopic" itemValue="#{selectedTopic.id}" itemLabel="#{selectedTopic.topicName}" />
            </h:selectOneMenu>

Just notice, that when subject selectonemenu changes, then the topics menu change according to subject ID. I had create a simple function inside Topics Managed Bean (the managed bean for the child selectonemenu ) by editing the hibernate getList() function like as under:

public List<Topics> getTopicsListBySubjectId(String subjectID) 
    {
        Topics topic = new Topics();
        List<Topics> TopicsList = new ArrayList<Topics>();

        if(subjectID.length() != 0)
        {
            topic.setSubjectId(Integer.parseInt(subjectID));
            TopicsList = getTopicsService().getTopicsBySubjectId(topic);
        }
        else
        {   
            TopicsList.addAll(getTopicsService().getTopics());
        }
        return TopicsList;
    }

and things worked like a charm.... :)

Question 3

It is just example. Try to reference for your program.

example.xhtml

        <p:selectOneMenu value="#{SelectOneMenuBean.selectedValue}" 
                         style="width:195px;" required="true" id="countryMenu">
            <p:ajax update="cityMenu"/>
            <f:selectItems value="#{SelectOneMenuBean.countries}"/>
        </p:selectOneMenu>
        <p:selectOneMenu style="width:195px;" required="true" id="cityMenu">
            <f:selectItems value="#{SelectOneMenuBean.cities}"/>
        </p:selectOneMenu>

SelectOneMenuBean.java

@ManagedBean(name="SelectOneMenuBean")
public class SelectOneMenuBean {
    private String selectedValue;

    public String getSelectedValue() {
        return selectedValue;
    }

    public void setSelectedValue(String selectedValue) {
        this.selectedValue = selectedValue;
    }

    public String[] getCountries() {
        return new String[] {"AAA", "BBB", "CCC", "DDD"};
    }

    public String[] getCities() {
        if(selectedValue != null && selectedValue.equals("AAA")) {
            return new String[] {"City_1 of AAA", "City_2 of AAA", "City_3 of AAA"};
        } else if(selectedValue != null && selectedValue.equals("BBB")) {
            return new String[] {"City_1 of BBB", "City_2 of BBB", "City_3 of BBB"};
        } else if(selectedValue != null && selectedValue.equals("CCC")) {
            return new String[] {"City_1 of CCC", "City_2 of CCC", "City_3 of CCC"};
        } else if(selectedValue != null && selectedValue.equals("CCC")) {
            return new String[] {"City_1 of CCC", "City_2 of CCC", "City_3 of CCC"};
        } 
        return new String[] {"No City"};
    }
}

Question 4

I know a solution for RichFaces, I'm pretty sure it will works for PrimeFaces as components are almost the same :

http://showcase.richfaces.org/richfaces/component-sample.jsf?demo=ajax&sample=selectsUpdates&skin=blueSky

EDIT : Here is the translation applied to your code :

<h:outputLabel value="Estado" styleClass="requiredLbl"/>
<p:selectOneMenu id="Estado" value="#{beanInscripcion.id_estado}" valueChangeListener="#{beanInscripcion.buscarMunicipios(event)}" >  
    <f:selectItem itemLabel="Elegir Estado" itemValue="" />
    <f:selectItems value="#{beanInscripcion.estados}" var="edo" itemLabel="#{edo.nombre_estado}" itemValue="#{edo.id_estado}" />  
    <p:ajax update="second" process="@this" listener="#{beanInscripcion.buscarMunicipios(event)}" />
</p:selectOneMenu>
<p:separator />
<p:outputPanel id="second">
    <h:outputLabel rendered="#{not empty beanInscripcion.id_estado}" value="Municipio" styleClass="requiredLbl"/>
    <p:selectOneMenu rendered="#{not empty beanInscripcion.id_estado}" id="Municipio" value="municipio">  
        <f:selectItems value="#{beanInscripcion.municipios}" var="mun" itemLabel="#{mun.nombre_municipio}" itemValue="#{mun.nombre_municipio}" />  
    </p:selectOneMenu>
</p:outputPanel>

And for the bean :

@ManagedBean(name = "beanInscripcion") @RequestScoped public class BeanInscripcion implements Serializable {

static String strURL;
private List<Estado> estados; 
private List<Municipio> municipios;
private int id_estado;
public BeanInscripcion() throws SQLException{
        estados = new ArrayList<Estado>();
        buscarEstados();
}

public void buscarEstados() throws SQLException {
    Connection connection = getConnection();
    Statement statement = connection.createStatement();
    ResultSet result = statement.executeQuery("SELECT * FROM estado");
    result.beforeFirst();
    while (result.next()) {
        Estado estado = new Estado();
        estado.setId_estado(result.getInt("id_estado"));
        estado.setNombre_estado(result.getString("nombre_estado"));
        estados.add(estado);
    }
}

public void buscarMunicipios() throws SQLException {
    Connection connection = getConnection();
    Statement statement = connection.createStatement();
    ResultSet result = statement.executeQuery("SELECT id_municipio, nombre_municipio FROM municipio WHERE Estado_id_estado = '" + id_estado + "'");
    result.beforeFirst();
    while (result.next()) {
        Municipio municipio = new Municipio();
        municipio.setId_municipio(result.getInt("id_municipio"));
        municipio.setNombre_municipio(result.getString("nombre_municipio"));
        municipios.add(municipio);
    }
}

public Connection getConnection() {
    try {
        strURL = "jdbc:mysql://localhost:3306/mydb";
        Class.forName("com.mysql.jdbc.Driver");
        return DriverManager.getConnection(strURL, "root", "root");
    } catch (SQLException ex) {
        return null;
    } catch (ClassNotFoundException ex) {
        return null;
    }
}

public List<Estado> getEstados() {
    return estados;
}

public void setEstados(List<Estado> estados) {
    this.estados = estados;
}

public List<Municipio> getMunicipios() {
    return municipios;
}

public void setMunicipios(List<Municipio> municipios) {
    this.municipios = municipios;
}

public int getId_estado() {
    return id_estado;
}

public void setId_estado(int id_estado) {
    this.id_estado = id_estado;
}

}

Hope it will work since it is not tested!