How to not show the stdout output of a running process

On Linux, assuming you want to know what is writing to the same resource as your shell's stdout is connected to, you could do:

strace -fe write $(lsof -t "/proc/$$/fd/1" | sed 's/^/-p/')

That would report the write() system calls (on any file descriptor) of every process that have at least one file descriptor open on the same file as fd 1 of your shell.

Use the jobs built-in to see running tasks for your current shell.

$ ping google.com >/dev/null 2>&1 &
[1] 32406

$ jobs
[1]+  Running                 ping google.com > /dev/null 2>&1 &

$ ping google.com
[...]
^Z
[2]+  Stopped                 ping google.com

$ jobs
[1]-  Running                 ping google.com > /dev/null 2>&1 &
[2]+  Stopped                 ping google.com

To kill all running jobs, you can leverage jobs -p which lists the pids of all jobs.

$ for job in $(jobs -p); do kill $job; wait $job; done

Further reading: http://www.tldp.org/LDP/abs/html/x9644.html