Did I compile with OpenMPI or MPICH?

Question 1

The following diagnostic procedure assumes that MPICH/MPICH2 and Open MPI are the only possible MPI implementations that you may have linked with. Other (especially commercial) MPI implementations do exist and may have different library names and/or library symbols.

First determine if you linked dynamically:

% ldd my_executable
        linux-vdso.so.1 =>  (0x00007ffff972c000)
        libm.so.6 => /lib/libm.so.6 (0x00007f1f3c6cd000)
        librt.so.1 => /lib/librt.so.1 (0x00007f1f3c4c5000)
        libpthread.so.0 => /lib/libpthread.so.0 (0x00007f1f3c2a7000)
        libc.so.6 => /lib/libc.so.6 (0x00007f1f3bf21000)
        /lib64/ld-linux-x86-64.so.2 (0x00007f1f3c969000)

If you see libmpich.so in that list, then you have dynamically linked to MPICH (or MPICH2). If you see libmpi.so then you have linked with Open MPI.

If neither is present, then you probably just linked statically. In that case we need to examine the binary to look for distinguishing symbols:

% ( nm my_executable | grep MPIR_Free_contextid >/dev/null ) && echo "MPICH"
% ( nm my_executable | grep ompi_comm_set_name >/dev/null ) && echo "Open MPI"

Question 2

Open MPI applications react to MCA parameters, that can be passed in environment variables. Just run the executable in singleton mode (i.e. without mpirun/mpiexec) with something like sysinfo_base_verbose set to 30:

$ OMPI_MCA_sysinfo_base_verbose=30 ./program

If you get an output like:

[hostname:pid] mca: base: components_open: Looking for sysinfo components

then this is more than robust indication that the executable uses Open MPI.