How to address the error: cannot open source input file "core_m3.h": No such file or directory?
Perhaps find the file in your system, probably in a CMSIS directory, and then make sure your project actually lists that directory as part of the "Include Paths" so the tools can find the file.
for example, see:
devzone.nordicsemi.com/.../184681
Note that this is standard 'C' (and C++) programming stuff - not specific to Keil, or ARM, or embedded.