When we say "$manager->start and next;" , doesn't what is below this statement (rest of the for loop that is) get skipped completely?
The and isn't just a "do this then this", it's a shortcut operator. If the $manager->start evaluates to something true, it does the next, but otherwise it doesn't.
In the particular case of Parallel::ForkManager, the ->start method returns values just like fork does; in the parent, it returns the pid of the child (which is a positive integer, and thus true), and in the child, it returns 0 (which is false).
So, the result is that in the parent process, the next happens, and it goes around and spawns off the next one (which is what you want the parent to do). In the child, since the ->start returns a false value, the and isn't followed, and it goes ahead and does the bits of actual work. The child does its thing (with system in this case), and then calls the ->finish method, which is equivalent to exit, so the child doesn't go back to the top of the loop and try spawning off more children (that's the parent's job).