yes, yes, and yes. You do not have the right to use copyrighted music in any form unless you have paid for a licensing agreement.
Music Bed has inexpensive license for event videographers. But, I couldn't tell you if taking that licensed material and remixing would violate the agreement. I'm not sure on that even though I wouldn't see it being a problem if you paid for the right to use it.
Owner / Director / Editor
Video Marketing Toolbox.net
Canon 5D Mark II
with Final Cut Studio Adobe CS6 Production