I don't understand what you mean by part (a)but there are two ways to take care of vibration in a structure. The first is to make the existing structure stiff so that the vibration goes direct thru to the foundation. (heavy up the connections/beams/columns, etc.) the second is to make the...
I took civil/structural and found that the best thing that I did was to do as many problems that I could get my hands on. I found the Lindberg series to be an excellent reference - great index. I also had the practice exam problems. Problems, problems, problems, after that do some more.
The website www.heatinghelp.com should help you out on this question. I would think that yo would lose heat to the existing slab if it is not insulated.