Are there any specific .h files where we can refer to this method that needs to be used ( ex: evp.h )?
#include "openssl/evp.h" should be enough to get the EVP APIs. You will need other includes for other parts of OpenSSL but that covers EVP well enough.
still, are there any files that we can go through once before calling in the fips mode?
Turn on -Wdeprecated or equivalent in your compile and the low level calls will be flagged. They should all be deprecated.
One more doubt is How can we set fips enabled for the complete application (process/service) while running so that if we are using non-compliant algorithms/methods it should throw errors? Is it possible in OpenSSL 3.0.x?
The call you are looking for is:
EVP_set_default_properties(libctx, "fips=yes");
I strongly suggest reading the documentation about the FIPS provider and the migration guide. Both the avoidance of low level calls and setting the default properties are covered therein. There are a number of other nuances to trip over when using the FIPS provider.
Paul Dale