Presenter

Yes! I haven’t tested it with every remote of course, but all of them that I
have tested have worked perfectly. My personal favorite is the
Logitech Professional Presenter R800

On the slide you want to add it to, click the “Show Advanced Slide Setting” link, then click the “Add Data Field” button.

For an image: Set the name of the field to ‘background’ and put the URL for the image in the value field.

For video: Set the name of the field to ‘background-video’ and you can add in comma separated URLs to various video sources, such as: //example.com/bearded-dragon-scares-kitten.mp4,//example.com/bearded-dragon-scares-kitten.webm,//example.com/bearded-dragon-scares-kitten.ogv

Absolutely. There are several default themes included, but you can also make
your own. If there is a “presenter” directory in your WordPress theme, Presenter
will look there for additional themes. All you need for a theme is a .css file
with a header like this:
/** Template Name: My Presenter Template */

The css file will be included and used in your slideshow.

Sure. You can use the presenter-themes filter to add your own theme wherever
it is. It is passed an array where the index is the path to the css file and the
value is the name of the theme. Just add your own like this:

add_filter( 'presenter-themes', 'add_my_custom_presenter_theme' );

function add_my_custom_presenter_theme( $themes ) {
    $themes['/path/to/my/theme.css'] = 'My amazing theme';
    return $themes;
}