I agree coaches don't rely on the star system and I believe the star system is really for the fans. However, I cannot believe that if a coaching staff internally rates two kids as equals and the sites have them rated individually as a 4* and a 3* that the coaching staff wouldn't take this into consideration when determining which recruit to pursue a little harder. The 4* will generally excite a fanbase more than a 3*, so the marketing of the recruit naming the school alone would have some impact, minimal, but some if all other things are equal.
They don't. Coaches could give a rats a$$ about the star ratings.
If two kids are equals and you want to devote more time to recruiting one, it comes down to recruiting area, that high school, relationship with the coach, etc. It is pretty rare for two kids to be equal in the eyes of the staff where the kids' attributes don't break the ties (hgt/wgt, grades, overall speed, etc)
The value these recruiting sites have to coaches are articles with quotes, most provide contact information for the individual player and getting the exact measurements and speeds from when a player camped somewhere sponsored by that site.
As it relates to videos, the only ones that really matter are drill videos that show how a kid moves. Highlight videos are borderline useless b/c every kid looks like a BCS level kid, though you should probably take a look at them if you don't have game film from the time the highlight video takes place. You can occasionally gleam some athleticism related things, but game film is infinitely more important.