Win APIs on windows 8

Dear Experts,

I'm doing my migration of my own coding application (C++) from Win XP to Win 8.
I'm concerning the Win APIs compatibility.
The main question is "Will my used API work well on Win 8 as same as it used to do on Win XP".

I found that, in Win XP (C:\Windos\System32\) there's some dll like user32.dll, kernel32.dll,....
But in windows 8 (C:\Windows\System32), there're:
   +  not only user32.dll and kernel32.dll
   +  but also api-ms-win-....dll and \downlevel\api-ms-win-....dll (such as api-ms-win-core-heap-l1-1-0.dll)
So, please explain me,
   +  What's api-ms-win-....dll stand for?
   +  Does this make any trouble to compatibility of Win APIs.

Regarding your soon responses.
With best regards.