How to use getBeforeGroupsConfigurationMethods method of org.testng.Interface ITestMethodFinder class

Well, uh, it was more simple than I thought, and as is often the case I find the solution only once I've asked the question...

Anyway, the solution is to create an abstract base class which initializes the toolkit for you and it is as "easy" as this:

@Test
public abstract class JavafxViewTest
{
    @BeforeClass
    public static void initToolkit()
        throws InterruptedException
    {
        final CountDownLatch latch = new CountDownLatch(1);
        SwingUtilities.invokeLater(() -> {
            new JFXPanel(); // initializes JavaFX environment
            latch.countDown();
        });

        // That's a pretty reasonable delay... Right?
        if (!latch.await(5L, TimeUnit.SECONDS))
            throw new ExceptionInInitializerError();
    }
}

In which directory I to place my testng.xml file.....

I suspect that the testng.xml file should be put at the top of your classpath. If you are using maven then a good place for it would be src/test/resources/testng.xml. See this example:

How to call testng.xml file from pom.xml in Maven

is there any maven specification I have to make in pom.xml for detecting that testng.xml file is there and they have to read it.

I'm not 100% sure about this. In looking at the above example it looks like something like the following is recommended:

<plugin>
    <groupId>org.apache.maven.plugin</groupId>
    <artifactId>maven-surefire-plugin</artifactId>
    <version>2.12</version>
    <configuration>
       <suiteXmlFiles>
           <suiteXmlFile>src/test/resources/testng.xml</suiteXmlFile>
       </suiteXmlFiles>
    </configuration> 
</plugin>

You should be able to do it in PowerMockito, yes.

Anyway, in JMockit, you usually would write a verification block like the following:

@Test
public void exampleTest(@Mocked AFinalClass mock)
{
    // Call the code under test which uses AFinalClass.

    new Verifications() {{ AFinalClass.someStaticMethod(); }};
}

No, you don't have to use a framework:

Dependency Injection

Of course you can use a framework too, As someone said you can use Spring Framework and use their annotations. Here you have a tutorial:

Dependency Injection with the Spring Framework

Make sure you added the jcommander.jar file to your classpath if you are using a project without maven. Make sure your project structure has a "TestNG" library that has only one testng.jar file inside it.

You can use an IAnnotationTransformer:

public class MyTransformer implements IAnnotationTransformer {

  public void transform(ITest annotation, Class testClass, Constructor testConstructor, Method testMethod) {
    if (!annotation.getEnabled()) {
      System.out.println(testClass != null ? testClass : testMethod);
    }
  }
}

You could also check imports for imported Test annotation, should be:

import org.testng.annotations.Test;
@Test
public myTest(){ ... }

and not for example:

import org.junit.Test;

You need to initialize your WebDriver first. As I seeing you are creating the reference of WebDriver but not initialized, try as below :-

WebDriver driver = new ChromeDriver(); //or other driver which you want

Note :- If you want to initialize ChromeDriver you need to download chromedriver and set system property before initialize driver as :-

System.setProperty("webdriver.chrome.driver", "path/to/chromedriver");

So details answer like as below :-

public class VendorsHomePageTest 

{
    public WebDriver driver;
    @Test
    public void verifyVendorsHomePageTest() throws Exception
    {
        System.setProperty("webdriver.chrome.driver", "path/to/chromedriver");
        driver = new ChromeDriver(); //or other driver which you want

        LoginIntoVendors login=PageFactory.initElements(driver, LoginIntoVendors.class);

        login.verifyLoginVendors();

        VendorsHomePageApp vhpapp= PageFactory.initElements(driver, VendorsHomePageApp.class);

        //driver.manage().timeouts().implicitlyWait(10, TimeUnit.SECONDS);

        Thread.sleep(3000);

        vhpapp.clickOnNotificationsTab();

        vhpapp.clickOnProfileTab();

        vhpapp.clickOnTendersTab();

        vhpapp.clickOnDashboardTab();

        vhpapp.clickOnFirstTender();

    }

}

Edited :- You need to create separate class which gives you WebDriver instance as below :-

public class DriverInit {

    public WebDriver driver;
    private static DriverInit driverInit = null;

    public static DriverInit getInstance() {
        if (driverInit == null) {
            driverInit = new DriverInit();
        }
        return driverInit;
    }

    private DriverInit() {
        this.driver = new FirefoxDriver();
        this.driver.manage().timeouts().implicitlyWait(10, TimeUnit.SECONDS);
        this.driver.get("******");
    }

    public WebDriver getDriver() {
        return this.driver;
    }

now you can call it into LoginIntoVendors as below :-

public class LoginIntoVendors 
{
    @Test
       public void verifyLoginVendors() throws Exception
       {
           WebDriver driver = DriverInit.getInstance().getDriver();

           IntiationPage vendorInit=PageFactory.initElements(driver, IntiationPage.class);

           vendorInit.clickOnLoginButton();

           VendorsLoginAction Loginven=PageFactory.initElements(driver, VendorsLoginAction.class);

           Loginven.vendorlogin("***","***@gmail.com", "****");

           String title = driver.getTitle();
           System.out.println("Title is  :" + title  );


       }
}

and in the VendorsHomePageTest as below :-

public class VendorsHomePageTest 

{
    public WebDriver driver;
    @Test
    public void verifyVendorsHomePageTest() throws Exception
    {

        driver = DriverInit.getInstance().getDriver();

        LoginIntoVendors login=PageFactory.initElements(driver, LoginIntoVendors.class);

        login.verifyLoginVendors();

        VendorsHomePageApp vhpapp= PageFactory.initElements(driver, VendorsHomePageApp.class);

        //driver.manage().timeouts().implicitlyWait(10, TimeUnit.SECONDS);

        Thread.sleep(3000);

        vhpapp.clickOnNotificationsTab();

        vhpapp.clickOnProfileTab();

        vhpapp.clickOnTendersTab();

        vhpapp.clickOnDashboardTab();

        vhpapp.clickOnFirstTender();

    }

}

Hope it helps..:)

There is a no way that testng plugin can automatically figure out.

You can set your testng preferences at the workspace or project level. If you set it at the workbench level then for all projects, by default, testng would put the results there.

Go to Window->Prefs->TestNG.
Change Output directory to be same as maven output directory.