1) Your keyboard appears to be broken. Perhaps you would like to fix it.
2) Yes, they are completely compatible (though there really isn't any reason to go with anything other than windows 7 x64 in any new build).
I would not recommend using Win XP with a Core i3/5/7 machine.
Win XP Home is only for single core CPUs. Win XP Pro has SMP, which can recognise multiple CPUs. But XP was released in 2001, and back then multi-core didn't exist, only multi-socket CPUs (2 CPUs each in it's own socket).
Windows 7 would recognise and properly use multi-core CPUs.
Win XP Home is only for single core CPUs. Win XP Pro has SMP, which can recognise multiple CPUs.
These two sentences are unrelated and the first is completely wrong. Win XP Home is entirely capable of using 8 threads, just like Pro. SMP has nothing to do with that. SMP is for multiple CPUs in separate sockets. If you're running such a system then the chances are you're not an average user and should not be using Home.