OK, it's like this.

I have just bought this new Schecter 7 String (C7 Hellraiser), got it set up and everything, but here is the thing.

Each time i PM a string and pick it, all of the strings vibrate as well making a
not so clean playing experience.

This did not happen on my old 6 string. I was wandering if you could give me some advice
as for what can i do about it... could it have something to do with the bridge height?

My advice is take it back to wherever you got it setup and ask them to do it properly this time. Don't pay for shit work.

Are you totally positive it's a result of a bad setup?