This then raises another question, does the latter in fact depend on services provided by the former, or a similar government site that has been DDOS'd? This is possible, perhaps they are even cohosted in a data centre somewhere and taking down one will take down another.
Assuming you go ahead then at this point you are basically engaged in attacking the infrastructure (possibly civilian) of a foreign nation at a time of war, presumably from a NATO country. Now you're doing this as a private individual, and your government would probably dissavow any knowledge of your actions, but there's always the chance that the Russian's wouldn't believe you or decide to interpret your DDOS as an act of aggression performed on behest of your host nation and respond in kind, or even escalate up to and including the use of strategic thermonuclear weapons. While this may be an unlikely scenario the possible consequences are catastrophic, so is it ethical for you to risk the survival of global civilisation based on your need to be seen to do something? Probably not.
Absolutely. The government doesn't even allow low level officers to just randomly attack on their own recognizance.
Acting on your own is not only likely to be ineffective, you may harm the wrong people, you may interfere with serious operations, etc. Imagine a vigilante with a gun on a battlefield - they could compromise opsec, create obstacles, become a distraction, etc. for an existing operation. Nobody wants some untrained loner running around with a weapon.
A nation state may play tit-for-tat with another nation state but they will assess the consequences and act accordingly.
Your ISP might not be happy with the extra traffic though.
I'm glad you're at least thinking whether DDoS could be wrong. I've never encountered a situation where DDoSers were the good guys.