A YouTube FancyBox uses fancy-box(light-box) to show YouTube video in a popup box on click of thumbnail which is generated from YouTube video.
=> You need to add shortcode to you page, post or your text widget
=>Yes, It does it's in plugin submenu named as "YTubeFancyBox".
=>you can set default height and width at admin side
=>you can set default auto play option at backend
=>you can set height and width for each image thumbnail in shorcode
[youtube videoid=<videoid> height=<height> width=<width> ]
=>You can find youtube video id at backend by inserting youtube video url
=>Yes, you can add
[youtube url="<youtube video url here>" ]