Can a child process generated by fork() ever have a process id lesser than its parent(without crossing the maximum limit)?
The PID is usually the next available value but anyhow can it possibly be less than the parent's PID?
Yes. PIDs are not guaranteed to be in any order. Some systems and some security extensions generate random PIDs to avoid attacks based on child PID prediction. Of course even systems that linearly generate PIDs need to wrap around at some point.