Are the Russian people willing to go to war?

Would not matter in the short-term.

And I'm sure enough can be brought around easily enough if it does end up mattering. Remember, the Russian people fell harder for the FSBs anti-vax psyops that almost anyone else even though that psyops was aimed primarily at the west.

not matter what his people want.

He and Trump share that trait: neither cares about the health, safety or welfare of their people.

not matter what his people want.

He and Trump share that trait: neither cares about the health, safety or welfare of their people.

It is the leaders of the country who determine the policy and it is always a simple matter to drag the people along, whether it is a democracy or a fascist dictatorship or a Parliament or a Communist dictatorship.
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voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same way in any country.

-Hermann Goering
"Nuremberg Diary" by Gustave M. Gilbert, 1947

If you're asking if this will harm Putin's standing with the Russian population, he doesn't care.

He squashes any dissent against him now with no regard for the public reactions.

Will they sacrifice their kids for war or try to flee to Europe/America?

Sadly, it's also one we're about to find out the answer to it appears.

And the Russian military proper will use proxies to the maximum degree possible, such as the separatist rebels in Eastern Ukraine trying to conscript at gunpoint every able bodied man they can get their hands on.

One of the lessons the Russian military learned from the Soviet misadventure in Afghanistan was the importance of hiding the true casualties. They have recently put that lesson into practice in the Chechnya and Georgia conflicts. They will no doubt do so again here, and their task will be aided by the fact that many of the deaths will occur amongst Russian-speaking Ukrainians used as cannon fodder such as the rebels and conscripts noted above.

The soldiers will do as they are ordered. The Russian People will be fed propaganda and dissent will be crushed.

In other words -- it doesn't matter what they want.

don't think Putin has taken the time to ask the soldiers and citizens of Russia that question. Then again I do not recall being asked if I wanted to fight in Vietnam.