Would this idea violate any law?

The idea is this :

My website would just embed videos from various websites like youtube, metacafe, etc.
I want to have users log in and comment or discuss on the videos I embed.
The purpose is that I have a set of audience that would be interested in particular type of videos and I gather those and put them all together (just like creating a channel on youtube except that I don't create the videos but compile them from various sources).

Also, If I'm doing that what and where do I mention that these contents are not mine and I'm just embedding them.

Would this infringe any copyright violation? Sorry if I sound dumb but doesn't hurt to ask right.

It's hard to answer without knowing how the product exactly works, but I can tell you I see two main legal issues here already.

1) Copyright issue related to the content of the videos. The classic problem of user generated content: what if somebody uploads the leaked Jay-Z video or upload something he created but with a non-original soundtrack without obtaining clearance / pay synch royalties.
Luckily, this problem is relatively easy to solve thanks to the DMCA safe harbor provisions. You can google that for more info on how to do it, but in short if you set up a takedown process for infringing material, you can escape liability.

2) Secure the right to source/republish content from other websites. Unfortunately, the only way to solve this is going to the TOS of each one of them and check if you have the right to do that. I think YouTube allows it, but there might be limitations.

I definitely recommend you check with your lawyer before starting this venture. I don't think he'll say "this is illegal"; he will probably blurb a complicated explanation that would not provide you with a clear answer. It is up to you, the entrepreneur, to ponder the legal information, assess the risks, and decide if it's worth or not. "Legal risk" is never zero.

{insert usual "this is not legal advice" disclaimer here}

There is a continuing legal battle over embedding content from other sites into your site. I will not even attempt to advise you legally. But I can tell you that Youtube has an embed link on the bottom of many of their videos. They seem to encourage embedding. I have seen where the embed link is disabled because the person uploading the video choose to disable it.