core: modernize execution code a bit

Among other things, avoid log_struct() unless we really need it.

Also, use "r" as variable to store function errors in, instead of "err".
"r" is pretty much what we use everywhere else, hence using the same
here make sense.

FInally, in the child, when we want to log, make sure to open the
logging framework first, since it is explicitly closed in preparation
for the exec().