Where I can get Selenium API documentaions?

We can find corresponding Selenium API documentations as below:

• Selenium HQ(user manual).
• Javadocs.
• Ruby docs.
• Python docs.
• C# docs.
• Javascript docs.

Perl and PHP bindings:

• Perl WebDriver bindings.
• Facebook - PHP bindings.
• For other PHP WebDriver bindings see either Google code or GitHub.

How I can select a value in dropdownlist that is not visible in selenium?

As display is set to 'none' for 'Select' tag, Selenium is unable to identify dropdown list values.
One way of handling is by clicking that dropdown and enabling the list.
Other way is by executing JavaScript to enable the dropdown list and then selecting value using WebDriver's 'Select' API.

Here is the code to handle using JavaScript:

 JavascriptExecutor js = (JavascriptExecutor)driver;
js.executeScript("document.getElementById('country').style.display='block';");

//Then Select required value
Select dropdown = new Select(driver.findElement(By.id("country")));
dropdown.selectByVisibleText("India");  

Assuming HTML code for select is as below:

Select Country
India 
United States