I don't really know what's their game, if they really think they can take on America.
I think they can take on America. Not in a straight, all-out US vs Iran war of course, but then that's not Iran's style. The history of US foreign interventions since WW2 gives context and lessons. Iran doesn't have to have tanks arranged on the White House lawn in order to win. There are other avenues. They are already causing oil prices to rise...
I remember there's some conspiracy theory circulating that China and Russia would support an aggression by Iran and when conflict starts, they all gang up on an overstretched America. How likely would that be?
Very unlikely I think to see an overt conflict between China/Russia and the US, but it's no secret that Iran is allied with both China and Russia. For example, they conducted a
joint naval drill in December.
Despite China's ever-growing role in world affairs, they have somehow managed to stay quite neutral so far in the chaos of the Middle East. I would imagine this is intentional rather than inadvertent. One concern I suppose is that the US/Iran thing might cause China to take a side, although again, whilst that is far more likely than an outright China/US conflict, I would still say it is unlikely overall.
Most likely I think is proxy attacks around the world against US interests, probably involving Hezbollah, and maybe involving covertly channeled Russian funding. Just speculation though, I'm no expert.