squeue to look at the list of running/queued or held jobs

sinfo to show which nodes are idle, busy or down

scontrol show node  to get more detailed information on a node

For problem nodes - indeed just log into any node to see what a healthy node looks like
systemctl status slurmd
cat /var/log/slurm/slurmd.log

On your slurm controller look at the slurmctld and slurmdbd logs