I would use HDMI for both Dish and Blu Ray if possible. If you only have one port get a cheap HDMI switch (and extra cables) online from somewhere like Monoprice or Amazon.
I believe you will. Some others have not mentioned HDCP when talking about blu-rays. If the player cannot communicate w/ the TV, it will not enable 1080p because it will think it isn't HDCP compliant... you're much better off to use HDMI over component.
Compoment and HDMI quality are the same. Component from Dish receiver is just fine. Regarding Blu-Ray you are correct...and I don't think any current players even have component outputs.