They don't print many dollars - less than 7% of dollars on the books exist as coin or currency.
Most dollars are created when loans are made - they exist as data entered on a ledger, maintained in computers. They are markers that represent a unit of value - like a "degree" on a thermometer.
Aren't oil prices inversely proportional to the value of the U.S. Dollar?
Relative to prices measured in other currencies, yes. The dollar has declined against the euro by 50% - thus, while prices in Europe have risen from $6 to $9, the prices in the United States have risen from $2 to $4 (doubled). (I didn't take the time to research the precise numbers, those are representative - fuel is still more expensive in Europe than it is in the United States).
Part of the price increase is supply and demand, part is from currency valuations.
The relationship of the value of the dollar, our economy, and our debt is quite complex. It is my opinion that the Fed is devaluing the dollar as a way of managing foreign debt - essentially the equivalent of writing off half the value of the debt held by China. The $1 trillion China holds is now worth half what it used to be worth ...
The same holds true with American debt - essentially, wealth is being transferred from those who trusted the United States government enough to loan their money to the government, to the benefits paid for by those dollars. As inflation rises, the future cost to pay back that debt falls - at the expense of the debt holder.
This lacks integrity - but it worked in the past to lower the United States' real debt, and it seems to be working now.
The risk of currency devaluation is the rise in price of imported goods, and the ability of foreign investment to buy real American property - such as the Belgium InBev beer company about to take over Anheuser Busch for $46 billion. That is only $29 billion euro, where 5 years ago that would have been $55 billion euro.
The advantage of currency devaluation is it makes American workers competitive again - lowering American costs and cutting the trade deficit, putting Americans back to work, and increasing the value of American real property (farmland, real estate, gold, etc.).