Getting featured image of particular size.

Please refer to the WP-Admin » Settings » Media. There you will find all the image sizes a theme creates. Basically the WordPress by default creates three sizes unless the Original:

• Large size (Default: 1024 x 1024)
• Medium size (Default: 300 x 300)
• Thumbnail size (Default: 150 x 150)

From the admin panel you can change their value too.

NOTE: Changing image dimensions can only work on new uploads after a successful save of the settings. Otherwise after a settings save you have to resize your images with a plugin like Regenerate Thumbnails by Viper007Bond.

A#2: Yes, the feature, unless the default three is basically Theme based.
A#1: You can call particular image sizes with <?php the_post_thumbnail('image-slug') ?>. And most the cases the image-slug, as I mentioned it, is the left-hand name of the size in the Media settings page.

NOTE: In general, code related to new image sizes are mentioned in the Theme’s functions.php with a function named add_image_size().
_{Syntax: <?php add_image_size( $name, $width, $height, $crop ); ?>}

Inspect and find accordingly if you fail with the Media settings’ image size names. Good luck!