The US is the biggest payer since 1945
This is such a tiny drop in the ocean - it really does not matter. I think the UN costs about $10B a year to maintain (including peacekeeping operations), and the US contributes about 20% of this, or $2 billion.
If China and Russia had some kind of assurance that America would only play by the rules of the UN, I'm sure they would happily pay America's share for the next 50 years with an immediate payment.
Whenever America begins to complain about paying for the UN, know it's a red herring. All it means is that at that moment in time the UN is irritating and inconvenient for the United States.
They and what army? And with what money?
Well, during the Korean War the United Nations managed to land 500,000 soldiers in Korea, and fight the war to a standstill. The UN is only as strong as people's faith in it.
If everybody believes in it, you don't need a large standing army or large budgets. It's enough that the 5 great powers on the Security Council have condemned your actions, and your life is now forfeit (Kuwait - 1991. Gorbachev voted with America on SC Resolution #678).
However, if the very members of the Security Council do everything in their power to ensure that it does not work properly, and that everyone views its resolutions as toothless - then yes, big problem.