Each and every one of their votes counts exactly the same as that of the US or Great Britain or Russia.
Yes, that's right. Except that the US still has unilateral veto ability, does it not? (Along with the other four original countries, IIR
Yes and no.
You have to distinguish between the General Assembly and the Security Council. In the GA, each country has 1 vote. Upper Volta matters there as much as the USA. In the SC, each of the 15 members has 1 vote. 5 of the members are permanent - the US, Britain, France, China and the Soviet Union, errrr, Russia. The other 10 rotate membership, sometimes to countries that matter a bit (like Germany or India or Brazil), and sometimes the Upper Volta types. The 5 permanent members also have a veto, so even a 14-1 vote fails to pass a measure if that 1 is from a permanent member. Otherwise, a simple majority wins.
Note, by the way, that in order to be eligible to be a member of the Security Council, a nation must be a member of a regional group. For example, Denmark is a member of the European region, and is therefore eligible (even if not picked for many years at a time). The one and only country that is ineligible for Security Council membership is Israel - because its Arab neighbors utterly refuse to allow it to join the regional group to which they belong. Israel has asked the Europeans to admit it to their regional grouping, but they've refused. That's worse than taxation without representation.
The General Assembly passes feel good measures (for those passing them, that is - they usually don't feel good to the victim nations, chiefly Israel, Taiwan and the US, and previously including South Africa).
As for me, I subscribe to the "US out of the UN, UN out of the US" theory of diplomacy. The whole thing is a nest of thieves and brutal thug dictatorships, and is worse than useless.