ERROR Could not open connection and user root

These errors are happening below in my application:

Note: I'm using Maven.

Here is an image of how the project structure is in eclipse:

Followtheerrorsbelow:

Follow persistence.xml :

<persistence xmlns="http://java.sun.com/xml/ns/persistence"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://java.sun.com/xml/ns/persistence
     http://java.sun.com/xml/ns/persistence/persistence_2_0.xsd"
    version="2.0">

    <persistence-unit name="fabricaweb2db" transaction-type="RESOURCE_LOCAL"> 
        <!-- provedor/implementacao do JPA -->
        <provider>org.hibernate.ejb.HibernatePersistence</provider>

        <properties>
            <!-- dados da conexao --> 
            <property name="javax.persistence.jdbc.url" value="jdbc:postgresql://localhost:5432/fabricaweb2db"/>
            <property name="javax.persistence.jdbc.driver" value="org.postgresql.Driver" />
            <property name="javax.persistence.jdbc.user" value="root"/>
            <property name="javax.persistence.jdbc.password" value="root"/>  
            <property name="hibernate.dialect" value = "org.hibernate.dialect.MySQLDialect"/>
            <!-- atualiza o banco, gera as tabelas se for preciso -->
            <property name="hibernate.hbm2ddl.auto" value="update"/>

        </properties>
    </persistence-unit>
</persistence> 

Follow pom.xml

<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
    <modelVersion>4.0.0</modelVersion>
    <groupId>br.com.fabricaprogramador</groupId>
    <artifactId>fabricaprogramador</artifactId>
    <version>0.0.1-SNAPSHOT</version>
    <packaging>war</packaging>

    <!-- Dependdecias do Hibernate -->

    <dependencies>

        <!-- Núcleo do Hibernate -->
        <dependency>
            <groupId>org.hibernate</groupId>
            <artifactId>hibernate-core</artifactId>
            <version>4.2.6.Final</version>
            <scope>compile</scope>
        </dependency>
        <!-- Implementação de EntityManager da JPA -->
        <dependency>
            <groupId>org.hibernate</groupId>
            <artifactId>hibernate-entitymanager</artifactId>
            <version>4.2.6.Final</version>
            <scope>compile</scope>
        </dependency>

        <dependency>
            <groupId> org.hibernate </groupId>
            <artifactId> hibernate-validator </artifactId>
            <version> 4.3.0.Final </version>
        </dependency>

        <dependency>
            <groupId>org.hibernate</groupId>
            <artifactId>hibernate-commons-annotations</artifactId>
            <version>3.2.0.Final</version>
        </dependency>

        <dependency>
            <groupId>org.hibernate.javax.persistence</groupId>
            <artifactId>hibernate-jpa-2.0-api</artifactId>
            <version>1.0.1.Final</version>
        </dependency>

        <dependency>
            <groupId>javax.transaction</groupId>
            <artifactId>jta</artifactId>
            <version>1.1</version>
        </dependency>

        <dependency>
            <groupId>org.hibernate</groupId>
            <artifactId>hibernate-jpamodelgen</artifactId>
            <version>1.1.1.Final</version>
            <scope>provided</scope>
        </dependency>

        <!-- Driver jdbc do postgresql -->
        <dependency>
            <groupId>postgresql</groupId>
            <artifactId>postgresql</artifactId>
            <version>9.1-901-1.jdbc4</version>
        </dependency>

        <dependency>
            <groupId>org.slf4j</groupId>
            <artifactId>slf4j-log4j12</artifactId>
            <version>1.7.7</version>
            <exclusions>
                <exclusion>
                    <artifactId>log4j</artifactId>
                    <groupId>log4j</groupId>
                </exclusion>
            </exclusions>
        </dependency>

        <dependency>
            <groupId>org.slf4j</groupId>
            <artifactId>slf4j-api</artifactId>
            <version>1.7.7</version>
        </dependency>


    </dependencies>

    <build>
        <finalName>fabricaweb2</finalName>
        <plugins>
            <plugin>
                <artifactId>maven-compiler-plugin</artifactId>
                <configuration>
                    <source>1.8</source>
                    <target>1.8</target>
                </configuration>
            </plugin>
        </plugins>
    </build>
</project>

The class TesteHibernate follows:

package fabricaweb2;

import javax.persistence.EntityManager;
import javax.persistence.EntityManagerFactory;
import javax.persistence.Persistence;

import br.com.fabricaprogramador.entidades.Usuario;

public class TestHibernate {

    public static void main(String[] args) {
        // Fabrica de EntityManagerFactory
        EntityManagerFactory emf = Persistence.createEntityManagerFactory("fabricaweb2db");
        // Gerenciador de entidades
        EntityManager em = emf.createEntityManager();


        // Inicando a Transação
        em.getTransaction().begin(); 
        // Cria o Objeto Usuario 
        Usuario usuario = new Usuario(); 
        usuario.setNome("Pedro"); 
        usuario.setLogin("p");  
        usuario.setSenha("234"); 

        // Prepara a instrução SQL 
        em.persist(usuario);
        // Confirmando a transação, fazendo a persistencia no banco 
        em.getTransaction().commit();

    }
}

The class Usuario follows:

package br.com.fabricaprogramador.entidades; 

import java.io.Serializable;

import javax.persistence.Entity;
import javax.persistence.GeneratedValue;
import javax.persistence.GenerationType;
import javax.persistence.Id;

@Entity
public class Usuario implements Serializable{ 

    @Id 
    @GeneratedValue(strategy=GenerationType.AUTO)
    private Integer id; 
    private String nome;
    private String login;
    private String senha;

    public Integer getId() {
        return id;
    } 
    public void setId(Integer id) {
        this.id = id;
    }
    public String getNome() {
        return nome;
    }
    public void setNome(String nome) {
        this.nome = nome;
    }
    public String getLogin() {
        return login;
    }
    public void setLogin(String login) {
        this.login = login;
    }
    public String getSenha() {
        return senha;
    }
    public void setSenha(String senha) {
        this.senha = senha;
    }
    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result + ((id == null) ? 0 : id.hashCode());
        result = prime * result + ((login == null) ? 0 : login.hashCode());
        result = prime * result + ((nome == null) ? 0 : nome.hashCode());
        result = prime * result + ((senha == null) ? 0 : senha.hashCode());
        return result;
    }
    @Override
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Usuario other = (Usuario) obj;
        if (id == null) {
            if (other.id != null)
                return false;
        } else if (!id.equals(other.id))
            return false;
        if (login == null) {
            if (other.login != null)
                return false;
        } else if (!login.equals(other.login))
            return false;
        if (nome == null) {
            if (other.nome != null) 
                return false;
        } else if (!nome.equals(other.nome))
            return false;
        if (senha == null) {
            if (other.senha != null)
                return false;
        } else if (!senha.equals(other.senha))
            return false;
        return true;
    }   

}