What all validations should be performed for confirming whether storm is installed and working properly .
You should make sure you're running HA fr Nimbus, at least 3 zookeeper servers and multiple supervisors. for some time, Nimbus was single point of failure and once down, you'd lose ability to control job behavior but that's been fixed in recent versions of Stprm, you can now enable HA via Ambari https://hortonworks.com/blog/fault-tolerant-nimbus-in-apache-storm/
So at the minimum, run 2 Nimbus servers, 3 zookeepers and as many supervisors as you can to maintain parallelism. I cannot find reference in our docs to set this up but once you are on Storm config page, there should be an option to add a standby Nimbus. Once up, you can submit a topology and simulate a Nimbus fail over, zk and supervisor fail over, adjust as necessary and continue tests.