How to verify if iptables is running or the firewall is activated

There is no such thing as "iptables is running" - there is no dedicated firewall process to monitor.

If the kernel modules are loaded and rules defined (both of which are proven by showing a valid rules table), the filtering is active. It is done in-kernel on events (packet rcv/snd) and not on a separate process.

So: Yes, if the rules shown are what you want, then your firewall is up.