I think you're getting well into the realms of fantasy here, firstly Russia has a huge nuclear arsenal including subs and mobile ground-based launchers, it would be very difficult if not near impossible for the even US to attempt to strike and take out all of them without likely risking MAD in the process, China has a more modest arsenal and far less conventional capability, it would have pretty much no chance, it would be suicidal.
Not to mention they don't really have any motivation to do so and they have an explicit no first strike policy.
If Russia starts activating its strategic forces though, regardless of any policy they may or may not proclaim to have, regardless of any target they might seem to be intending to strike like Ukraine, it is going to have a lot of people getting very itchy. There is potentially a point where countries like the US have no options which aren't a gamble. Which is one of the reasons I can't see Russia rushing to put its nuclear capabilities strategic or tactical into use.