I will like to know if embedding YouTube videos on my website consumes my bandwidth when the videos are being viewed.
I found a good answer for you from this Stack Overflow question:
Both the youtube player and the video content is streamed from YouTube's server. The only price you pay is the few bytes it takes to add the video player embed code in your HTML pages.
Every element in your website which is pulled from other web servers wont consume your bandwidth. It's only the code for that element which is nothing but some bytes.