It is difficult to believe you are being objective when you begin your post by accepting the Russian position this is a proxy war being waged by the US against Russia rather than considering this may be a case in which US interests and Ukrainian interests align. Of course it is possible to oppose aid to Ukraine without supporting Russia, but I've never seen a compelling argument to support such opposition, however once one starts making claims Ukraine shouldn't be helped because it has a problem with corruption or because Zelensky is a cocaine addict or that he is stealing US aid money, then one is no longer looking out for US interests and is promoting Russian interests. So, on to your questions.
Is opposing Russia in Ukraine a vital American national strategic interest?
Absolutely. Neither the global economy nor the US economy can grow and prosper without international trade and international trade cannot flourish in the absence of internationally accepted rules of order. In the invasion of Ukraine, Putin violated all relevant international laws and treaties and has made clear he believes all land that ever belonged to Russia still belongs to Russia and he won't be stopped from claiming it by any laws or treaties, therefor an environment in which international trade can flourish cannot be reestablished until Russia's neo colonial ambitions are quelled. If not in Ukraine, then where?
What specifically is our objective in Ukraine, and how will we know when we’ve achieved it?
Our objective is to help Ukraine to force Russia out of Ukraine and to continue economic pressure until Russia accepts international rules of order so that the global economy and the US economy can continue to grow. We will all know when we have achieved that.
What is the limit of funding and material you would be willing to send to the government of Ukraine?
However much it takes to force Russia to stand down from its neo colonial ambitions that are disrupting the environment for international trade. It is impossible to state a dollar amount at this time, but I am confident that it will be less than allowing Russia to continue rampaging through eastern Europe and the Baltic states.
Should the United States support regime change in Russia?
Regime change for the better in Russia is very unlikely since all of Putin's challengers are either dead or in prison, but if a new government should come to power that embodied American values of Democracy and individual rights, then certainly the US should support it.
Given that Russia’s economy and currency are stronger than before the war, do you believe that U.S. sanctions have been effective?
It is not a given that the ruble and the Russian economy are stronger than they were before the war. The ruble has been manipulated by a Russian law forbidding Russians from exchanging it for dollars or euros and Russia demanding payment for oil and gas in rubles so its exchange rate does not indicate the strength of the Russian economy. According to the Russian Finance Ministry, Russia's oil and gas revenues for Jan and Feb are down by nearly 50% from last year, partly because of the sanctions. Yes, they are working.
"According to preliminary estimates, the volume of federal budget revenues in January 2023 amounted to 1.356 trillion rubles, which is 35% lower than the volume of revenues in January 2022," the Ministry of Finance says
tass.com
Do you believe the United States faces the risk of nuclear war with Russia?
We have faced that risk since the 1950's and then as now neither country can attack the other without being destroyed itself, so the risks remain minimal.
Let me add a question to your list. Why should the US play such an outsized role in maintaining international order?
The US economy is so much larger than the economy of any other nation and the US military is so much more powerful than that of any other nations and US leadership in world events is so much more respected than the leadership of any other free world country that it would be impossible to reestablish international rules of order in which international trade would flourish without the US playing a major role.