Do you think it's strategically possible to get into a shooting war with China and/or Russia, two nuclear-capable nations, and emerge meaningfully victorious? Does the F-35 change that? Why or why not?
It depends on the objectives. If your goal is to annex them, no.
If your goal is to deter a conflict, or fight a conflict over some remote piece of land where the war could possibly be contained, then maybe. Nobody has incentive to start a nuclear war, so it would likely stay conventional. Meaningful missile defense might also have an impact on the calculus - if a small nuclear strike could be reliably defeated that would probably make a foe less likely to try to escalate to a regional nuclear conflict (all in is just suicide).
However, it would be really costly for all sides, so the interest would have to be something actually worth fighting for. The US could probably deter a Russian invasion of Ukraine, for example, by stationing forces in Lithuania sufficient to threaten Moscow. The relative strength of both sides would probably allow a US victory (crazy thought), if the Russians didn't kill everybody on Earth, but it would depend on them actually allowing a US buildup, since we're separated by an ocean and resupply in that area would be very threatened by Russian Navy/Air/etc. Most likely there would be a Naval war, which could result in attacks on US ports/interior/etc, but on the whole the Russians don't have much of a navy these days and they wouldn't last too long.
But, like I said it would have to be an interest worth fighting for and the US really isn't going to risk even conventional bombs going off in DC and Manhattan and Saudi Arabia over Ukraine. So, all the above is really just a fantasy scenario. Maybe if somebody like Russia went really nuts going after US vital interests it would come to war, but that seems rather unlikely. But, on the other hand having modern weapons platforms only makes it less likely.