3. The oil prices are set by international traders. You believe it's not possible to influence them? And if you remember 1980-s then you remember that the only real value of dollar after the fall of Bretton Woods is the USA-Saudi agreement and fact that anybody who sells oil for anything except dollar will become democratic - Saddam wanted euros and Iraq is a democracy now. Qaddafi wanted a gold dinar and Libya is a democracy, too. Imagine how much Obama wants to bring democracy to Iran, Syria and Russia. Especially after the SPb, Russia oil exchange began trading oil for yuans.
The price of oil is set, like the price of all goods by supply and demand. There are two ways to influence the price of anything, alter supply or alter demand. Demand is set by many independent actors all buying things, this is very hard for any entity to control. Supply on the other hand is often controlled by a few entities, restrict supply the price goes up, allow more supply the price goes down. This was OPEC's game for years. The price of oil was sky high for years, encouraging more production, which in turn created more supply, which brings prices back down. Not to mention demand decreases as people were driven to more fuel efficient vehicles, and explored alternative energy sources. Add in tough economic conditions around the world causing a softening in demand, all of this combined to crater the price of oil. But that low price will spur demand and that will cause the price to go back up. I know it's not as sexy as a conspiracy theory, but supply and demand curves accurately describe the way prices are set. (Which isn't to say there AREN'T conspiracies, they usually focus on limiting supply however, and how successful they are usually comes down to solidarity).
Obama can't control the price of oil, if he could, he would have dropped the price before the midterm elections that saw his party loose control of the senate.
While it certainly benefits the US that many nations price oil in dollars, it is mostly because the dollar is a strong, stable currency, that maintains it's value. Nobody want's rupels or yuans when they can have dollars instead. Russia's current currency crisis is all that is needed to show why.
Many counrtires, including Russia and China keep reserves of US currency and bonds, to use to prop up their own currency if need be. This is also the only real reason to keep large gold reserves as well.
4. You keep dollar high and gold low. You cannot stop it. And it only means that Putin cheaply buys gold. And he buys gold nonstop. Russian gold resources still grow during all this crisis. Chinese do the same. Imagine how glad is Obama. And how much he wants to make oil cheaper.
I'm not entirely sure what you mean here, it doesn't make a whole lot of sense. The price of gold is up, not down. The dollar's strength is mostly due to the euro being week. Putin and the Chinese can buy all the gold they want, they can keep it in a big vault and swim in it Scrooge McDuck style, who cares?