The title of this post covers a lot of ground, but the answer is identical for all three cases.
The questions . . .
Would it be a good thing if interest rates rose?
Would it be a good thing if copper prices rose?
Would it be a good thing if the dollar appreciated?
. . . are all basically meaningless. In all three cases, the prices never change for no reason at all. In each case the real question is whether the thing that causes the price to change makes us better off or worse off.
In all three cases, the price/interest rate/exchange rate might rise due to strong economic growth in America. That would probably be a good thing. The exchange rate and the interest rate might rise due to tight money. That would be a bad thing if tight money were not appropriate at that time. Copper prices might rise because of civil wars in copper producing nations. That would be a bad thing.
This isn't just a minor problem; the economics profession is waste waist deep in reasoning from a price change. You can make a pretty good argument that reasoning from a price change caused the Great Recession. Most economists thought the fall in interest rates from August 2007 to May 2008 was caused by expansionary monetary policy. Not so. NGDP growth slowed, and if you are still one of those people who looks at how much money the government was actually producing, then the answer is the same. Growth in the monetary base basically stopped between August 2007 and May 2008.
The fall in interest rates from 5.25% in August 2007 to 2% in May 2008 was entirely due to a weak economy---the Fed had absolutely nothing to do with it. A more expansionary monetary policy that kept NGDP growth expectations at 5% would have led to a smaller fall in interest rates.
Almost every day I see examples of economists, including Nobel laureates, engaged in the EC101 mistake of reasoning from a price change. It needs to stop, as it is causing a lot of damage to the economy.
PS. Another misleading question is: "Should the government take steps to cause an increase in prices, interest rates or exchange rates?" The answer entirely depends on which steps they take. In late 2008, a government step to implement NGDPLT at 5% might have raised interest rates. In late 2008, an increase in the fed funds target might have raised interest rates. One would have been an expansionary policy, and the other would have been a contractionary policy. If you are simply talking about interest rates, you are not part of the solution; you are part of the problem.
PPS. And it does not help to mention "ceteris paribus". If ceteris are paribus, then prices do not change.