1. I doubt your project is going to go seamlessly. Compiling a bunch of applications from source can get quite tricky at times. Especially if you want to base it on a redhat system. Redhat likes to have weird locations for things and often has added it's own patches to things like compilers to make it work. These kind of difference always get you into trouble.
Whenever I want to compile applications I always go to
http://hints.linuxfromscratch.org/hints
Even though you don't have an LFS system there are usually things added in there that can be usefull for compiling on any distribution. Since you want to recompile most things anyway. Maybe it might be worth taking the consideration of going LFS all the way. It really helps to learn your system in and out and teaches you what each component does. Knowing that is very usefull for speeding up your system and illiminating stuff you don't need.
2. Just copy it like da Perp said
3. Doesn't matter which kernel you are running when you compile the programs. It should have the kernel headers which where used to compile glibc and the other programs in a different location. So if it uses any kernel headers then it should just get those.